PHYSIOLOGIC  OnricS 


DIOPTRICS  OF  THE  EYE,  FUNCTIONS   OF 

THE  RETINA  OCULAR  MOVEMENTS 

AND  BINOCULAR  VISION 


BY 

DR.     M.   TSCHERNING 

ADJUNCT-DIRECTOR  OF  THE  LABORATORY  OF  OPHTHALMOLOGY 
AT  THE  SORBONNE,   PARIS 


AUTHORIZED  TRANSLATION 

From  the  Original  French  Edition,  Specially  Revised  and  Enlarged 
by  the  Author 

BY 

CARL  WEILAND,  M.D. 

FORMER  CHIEF  OF  CLINIC  IN  THE  EYE  DEPARTMENT  OF  THE  JEFFERSON  MEDICAL 
COLLEGE  HOSPITAL  OF   PHILADELPHIA 


WITH  212  ILLUSTRATIONS 


THIRD  EDITION 


PUBLISHED   BY 

THE  KEYSTONE  PUBLISHING  CO. 

PHILADELPHIA,    II.    S.    A. 
1920 

All  rights  reserved 


COPYRIGHT,  1900 
COPYRIGHT,  1904 
COPYRIGHT,  1920 

PUBLISHED  BY  THE  KEYSTONE  PUBLISHING  Co. 


Entered  at  Stationer's  Hall,  London,  Eng. 


TRANSLATOR'S  PREFACE 


Physiologic  Optics  is  a  science  which,  on  the  one  side,  touches 
the  highest  philosophic  problems  of  the  human  mind  and,  on  the 
other  side,  keeps  in  intimate  contact  with  the  practical  work  of 
the  opthalmologist,  who,  in  his  daily  work  of  refraction,  can  be 
guided  safely  only  by  its  principles. 

Many  are  the  text-books  on  this  important  subject.  Some  are 
mere  compilations  of  older  facts  and  some  are  written  by  men 
that  soar  so  high  above  the  field  of  the  practical  work  of  the 
opthalmologist  that  their  abstract  scientific  investigations  lose 
almost  all  contact  with  these  practical  workers. 

The  present  book  is  neither  a  mere  compilation  nor  an  abstract 
theoretical  investigation,  but  a  collection  of  all  the  old  and  new 
scientific  facts  that  have  any  bearing  on  the  practical  work  of 
the  oculist  and  optician.  It  is  written  by  a  man  who  lately  has 
probably  done  more  original  work  in  this  line  than  any  other 
since  Helmholtz  and  Bonders,  and  who,  furthermore,  has  been 
in  constant  contact  with  practical  ophthalmology. — Dr.  M. 
Tscherning,  who  was  born  in  Denmark  in  1854,  studied  ophthal- 
mology at  Copenhagen  under  the  philosophic  mind  of  Hansen 
Grut.  Since  1884  he  has  been  adjunct-director  of  the  laboratory 
of  opthalmology  at  the  Sorbonne,  where,  since  the  deplorable 
disability  of  Javal,  he  himself  has  performed  the  functions  of  the 
director.  This  laboratory,  which  was  founded  in  1876  for  Javal, 
after  he  had  become  widely  known  by  his  translation  of  the 
Physiologic  Optics  of  Helmholtz,  has  given  a  new  impetus  to 
this  science  in  France. 

Here  Tscherning  has  made  all  his  important  original  investi- 
gations, especially  on  ophthalmometry,  the  catoptric  images  of 
the  eye,  astigmatism,  spherical  aberration  and  accommodation. 

in 


All  .this  original  work,  as  'Well  as  that  of  former  investigators, 
is  dfescffoetf 'ih* -this  b6oV"with  great  clearness  and  succinctness, 
almost  entirely  free  from  tedious  mathematical  encumbrances. 
Instead  of  long  formulae,  the  experiment  and  simple  geometrical 
deductions  are  employed  to  explain  the  observed  phenomena. 
The  translator  has  endeavored  to1  reproduce  the  clearness  and 
brevity  of  expression  of  the  original  as  much  as  possible.  How 
far  he  has  succeeded  in  this,  it  is  not  for  him  to  judge. 

This  English  edition,  as  has  been  indicated  on  the  title  page, 
contains  many  additions  in  the  text  by  Dr.  Tscherning,  who  has 
thus  brought  his  book  thoroughly  up  to  date.  The  few  notes, 
added  by  the  translator,  have  been  included  in  brackets  with  the 
letter  W>.  appended.  A  list  of  illustrations  and  an  index  have 
been  compiled  to  enhance  the  practical  value  of  the  book. 

It  is  true  that  some  of  the  ideas  expressed  by  the  author,  es- 
pecially those  about  the  use  of  mydriatics  for  ordinary  purposes 
of  refraction  and  the  use  of  spectacles,  are  not  in  accord  with 
current  views  about  these  subjects  on  this  side  of  the  Atlantic. 
But  even  those  who  cannot  agree  with  the  author  on  these 
questions,  will  find  many  new  facts  and  ideas  which  will  make 
a  study  of  the  book  of  great  interest  and  profit.  The  translator 
only  hopes  that  the  reader  may  experience  the  same  intellectual 
pleasure  that  he  felt  while  reading  and  translating  this  work  of 
one  of  our  greatest  investigators  in  the  field  of  physiologic  optics. 

CARL  WEILAND,  M.  D.,  Philadelphia,  U.  S.  A. 


IV 


TABLE  OF  CONTENTS 


BOOK  I 

OCULAR  DIOPTRICS 


CHAPTER  I 
OPTIC  PRINCPLES 

1.  Optic  Properties  of  Bodies 1 

2.  Rectilinear  Propagation  of  Light   1 

3.  Reflection  and  Absorption 2 

4.  Regular   Reflection    2 

5.  Plane  Mirrors.     Construction  of  the  Image 3 

6.  Concave  Spherical  Mirrors   4 

7.  Convex  Mirrors    7 

8.  Practical    Remarks     7 

9.  Refraction    9 

10.  Quantity  of  Light  Reflected.     Total  Reflection 10 

11.  Refraction  by  Plates  with  Plane  and  Parallel  Surfaces 11 

12.  Refraction  by  a  Prism 12 

13.  Refraction  by  a  Spherical  Surface 13 

14.  Infinitely  Thin  Lenses   17 

15.  Theory  of  Gauss   23 

Bibliography 32 


CHAPTER  II 
THE  OPTIC  SYSTEM  OF  THE  EYE 

16.  Optic  Constants  of  -ihe  Eye   33 

17.  Optic  System  of  the  Eye   38 

18.  Aperture  of  the  System  : 41 

19.  Point  of  Fixation.     Visual  Line 44 

20.  Optic  Axis.     Angle  a    45 

21.  Useful  Image 46 

Bibliography 46 


CHAPTER  III 
THE  FALSE  IMAGES  OF  THE  EYE 

22.  General   Eemarks    47 

23.  The  Images  of  Purkinje  48 

24.  Manner  of  Observing  the  Images  of  Purkinje  50 

25.  False  Images  of  the  Second  Order  54 

26.  Manner  of  Observing  the  Sixth  Image   54 

Bibliography    56 

CHAPTER  IV 
OPHTHALMOMETRY 

27.  Principles  of  Ophthalmometry   57 

28.  Methods  of  Doubling    59 

29.  The  Ophthalmometer  of  Javal  and  Schiotz 61 

30.  Results  of  the  Measurement  of  the  Cornea 66 

31.  Measurement  of  the  Angle  a  77 

32.  Determination  of  the  Position  of  the  Internal  Surfaces 80 

33.  Determination  of  the  Centers  of  the  Internal  Surfaces 83 

34.  Direct  Determination  of  the  Radii  84 

35.  General   Remarks    85 

Bibliography     87 

CHAPTER  V 
CIRCLES  OF  DIFFUSION 

36.  Definition    88 

37.  Line  of  )3ight    89 

38.  Accommodation     89 

39.  Experiment  of  Czermack,  Scheiner  and  Mile  90 

40.  The  Optometer  of  Thomas  Young 91 

41.  Effects  of  the  Stenopaic  Opening   92 

Bibliography     94 

CHAPTER  VI 
ANOMALIES  OF  REFRACTION 

42.  General  Remarks  95 

43.  General  Remarks  on  Ametropia  97 

44.  Optometers    100 

45.  Myopia     101 

46.  Choice  of  Spectacles    104 

47.  Treatment  of  Myopia 106 

48.  Hypermetropia    109 

49.  Aphakia    tf  111 

Bibliography    113 

vi 


CHAPTER  VII 
SPHERICAL  ABERRATION 

50.  Optic   Principles    114 

51.  Phenomena  Dependent  on  the  Spherical  Aberration  of  Lenses. . .  115 

52.  Aberration  of  the  Human  Eye.    Experiments  of  Volkmann 120 

53.  Experiments  of  Thomas  Young  121 

Bibliography 130 

CHAPTER  VIII 
CHROMATIC  ABERRATION 

54.  Optic   Principles    131 

55.  Chromatic  Aberration  of  the  Eye 133 

56.  Experiment  of  Wollaston    134 

57.  Results 135 

58.  Phenomena  of  Dispersion,  the  Pupil  being  Partly  Covered 136 

59.  Correction  of  Chromatic  Aberration    137 

Bibliography    137 

CHAPTER  IX 
REGULAR  ASTIGMATISM 

60.  Optic  Principles.     Astigmatism  Produced  by  the  Form  of  the 

Surfaces    138 

61.  Defects  of  the  Image 141 

62.  Astigmatic  Surfaces    142 

63.  Astigmatism  by  Incidence  143 

64.  Astigmatism  of  the  Human  Eye.    Historical 145 

65.  Physiologic    Astigmatism    146 

66.  Corneal  Astigmatism    147 

67.  Measurement  of  the  Corneal  Astigmatism 147 

68.  Regular  Corneal  Astigmatism   149 

69.  Relations  between  Ophthalmometric  and  Subjective  Astigmatisms  150 

70.  Astigmatic    Accommodation    155 

71.  Post-Operative  Astigmatism    156 

72.  Keratoconus    157 

73.  Symptoms  of  Astigmatism   158 

74.  Examination  of  Astigmatic  Patients   159 

Bibliography    163 


CHAPTER  X 
IRREGULAR  ASTIGMATISM 

75.  General  Remarks   164 

76.  Examination  of  the  Eye  with  a  Luminous  Point 165 

77.  Different  Forms  of  Irregular  Astigmatism 166 

78.  Rules  for  Analyzing  the  Figures  of  the  Luminous  Point 171 

Bibliography    175 

CHAPTER  XI 
ENTOPTIC  PHENOMENA 

79.  Manner  of  Observing  Entoptic  Phenomena   176 

80.  Analysis  of  Entoptic  Phenomena    180 

81.  Entoptic  Observation  of  the  Vessels  of  the  Retina 183 

82.  Other  Entoptic  Phenomena  186 

Bibliography 191 

CHAPTER  XII 
ACCOMODATION 

83.  Measurement  of  the  Amplitude  of  Accommodation   192 

84.  Mechanism  of  Accommodation   (Historical,  A)    195 

85.  Mechanism  of  Accommodation  (Historical,  B)    201 

86.  Personal  Experiments    206 

87.  The  Author 's  Theory  of  Accommodation 220 

Bibliography    228 

CHAPTER  XII 
OPHTHALMOSCOPY 

88.  Methods  of  Illuminating  the  Fundus  of  the  Eye 229 

89.  Examination  by  the  Erect  Image  232 

90.  Examination  by  the  Erect  Image.    Observations 237 

91.  Examination  by  the  Inverted  Image  241 

92.  Ophthalmoscopic  Examination  of  the  Refracting  Media 245 

93.  Skiascopy    246 

Bibliography    253 

CHAPTER  XIV 
THE  PUPIL 

94.  General  Remarks   254 

95.  Action  of  Mydriatics  and  of  Myotics 255 

96.  Movements  of  the  Pupil   256 

97.  Advantage  of  the  Position  of  the  Pupil  near  the  Nodal  Point . . .  259 
Bibliography    265 

viii 


BOOK  II 

FUNCTIONS  OF  THE  EETINA 


CHAPTEE  XV 

CHANGES  WHICH  THE  KETINA  UNDERGOES  UNDER  THE 
INFLUENCE  OF  LIGHT 

98.  Retinal  Purple   266 

99.  Movements  of  the  Pigment  Under  the  Influence  of  Light 267 

Bibliography    269 


CHAPTER  XVI 
THE  LIGHT  SENSE 

100.  Psychophysical  Law  of  Fechner   270 

101.  Measurement  of  the  Light  Sense  274 

102.  Results     278 

Bibliography    281 

CHAPTER  XVII 
THE  COLOR  SENSE 

103.  General  Remarks   282 

104.  Phenomena  of  Contrast  (Simultaneous)    287 

105.  After  Images   291 

106.  Phenomena  Dependent  on  the  Variation  of  the  Brightness  of 

the  Colors   293 

107.  Methods  of  Mixing  the  Colors  298 

108.  Results  of  the  Mixtures  of  Colors  301 

109.  Abnormal  Trichromasia   315 

110.  Color  Blindness  or  Daltonism  (Dichromasia)    317 

111.  Monochromasia    324 

112.  Clinical  Examination  of  the  Color  Sense 324 

113.  Hypotheses  on  the  Mechanism  of  Color  Vision 327 

Bibliography    332 

CHAPTER  XVIII 
THE  FORM  SENSE 

114.  Central  Visual  Acuity   334 

115.  Peripheral  Acuity   341 

Bibliography 345 

ix 


BOOK  III 

THE  OCULAB  MOVEMENTS  AND  BINOCULAR  VISION 

&•*, 

CHAPTER  XIX 
THE  LAW  OF  LISTING 

116.  Centers  and  Axes  of  Eotation  of  the  Eye 346 

117.  Law  of  Listing 348 

118.  Experiments  of  Meissner.    Apparently  Vertical  Meridian 355 

119.  Historical    358 

Bibliography    359 

CHAPTER  XX 

THE  OCULAR  MOVEMENTS 

\ 

120.  Jerking  Movements  of  the  Eyes 360 

121.  Relative  Movements  of  the  Two  Eyes 360 

122.  Measurement  of  Convergence   363 

1 23.  Relations  between  Accommodation  and  Convergence 365 

Bibliography    365 

CHAPTER  XXI 
PROJECTION  OF  VISUAL  IMPRESSIONS 

124.  Projection  Outwards  of  Uniocular  Vision  366 

125.  Projection  of  the  Visual  Field   366 

126.  Projection  in  Binocular  Vision    369 

Bibliography    376 

CHAPTER  XXII 
MONOCULAR  PERCEPTION  OF  DEPTH 

127.  Influence  of  Accommodation   377 

128.  Indirect  Judgment  of  Distance    377 

129.  Influence  of  the  Parallax   380 

Bibliography     381 


CHAPTER  XXIII 
BINOCULAR  PERCEPTION  OF  DEPTH 

130.  Influence  of  Convergence    382 

131.  The  Stereoscope  382 

132.  Effect  of  the  Stereoscope 388 

133.  Identical  Points  of  the  Retinae   391 

Bibliography    395 

CHAPTER  XXIV 
STRABISMUS 

134.  Different  forms  of  Strabismus  397 

135.  Measurement  of  Strabismus   400 

136.  Etiology  of  Concomitant  Strabismus   400 

137.  Vision  of  Strabismic  Patients   403 

138.  Treatment  of  Strabismus  404 

Bibliography    406 

CHAPTER  XXV 
OPTIC  ILLUSIONS 

139.  Optic  Illusions   407 

Bibliography 412 

Treatises  to  Consult   .                                                                       .  413 


LIST  OF  ILLUSTRATIONS 


no.  PAGE 

1.  Luminous  Source,  Opaque  Body,  Shadow  and  Penumbra 1 

2.  Eeflection  on  a  Plane  Mirror  3 

3.  Eeflection  on  a  Concave  Mirror  4 

4.  Eeflection  on  a  Concave  Mirror  5 

5.  Eeflection  on  a  Convex  Mirror  7 

6.  Construction  of  the  Utilized  Part  of  a  Mirror 9 

7.  Eefraction    9 

8.  Total   Eeflection    10 

9.  Prism  with  Total  Eeflection  11 

10.  Eefraction  by  a  Plate  with  Plane  Parallel  Surfaces 12 

11.  Eefraction  by  a  Prism  12 

12.  Eefraction  by  a  Spherical  Surface   13 

13.  Eefraction  by  a  Spherical  Surface   15 

14.  Eefraction  by  a  Parabolic  Surface    16 

15.  Construction  of  Image  Formed  by  a  Thin  Lens 18 

16.  Method  of  Measuring  the  Focal  Distance  of  a  Lens 21 

17.  Principal  and  Nodal  Points;  Anterior  and  Posterior  Focus 23 

18.  Construction  of  the  Image  of  an  Object 24 

19.  Construction  to  Find  the  Second  Principal  Plane 25 

19.o.  Construction  of  the  Cardinal  Points  of  Two  Optic  Systems 27 

20.  Construction  to  Find  the  Nodal  Points  of  a  Thick  Lens 28 

21.  Optic  System  of  the  Eye 33 

22.  Optic  System  of  the  Eye  of  an  Ox 34 

23.  Images  of  Purkinje  of  the  Eye  of  an  Ox  (Dead)   35 

24.  Double  Crystalline  Images  in  a  Case  of  False  Lenticonus 36 

25.  Diagram  of  the  Crystalline  Lens  36 

26.  Position  of  the  Cardinal  Points  of  the  Human  Eye  39 

27.  Pupil  of  Entrance  and  Pupil  of  Exit 43 

28.  Eeflections  and  Eefractions  by  a  Lens 47 

29.  Manner  in  which  a  Luminous  Eay  is  Divided  in  the  Eye 48 

30.  Position  of  the  Seven  Images  in  the  Eye 49 

31.  Corneal  Images  of  two  Lamps  Observed  with  the  Ophthalmo- 

phakometer 51 

32.  The  Ophthalmophakometer    53 

33.  Illustration  of  the  Principle  of  Doubling 58 

34.  Doubling  by  the  Two  Halves  of  an  Objective 59 

35.  Plates  of  Helmholtz   60 

36.  Doubling  by  an  Objective,  a  Central  Vertical  Band  of  which  has 

been  Eemoved    60 

.->7.     Prism  of  Wollaston    61 

xiii 


TIG.  PAGE 

38.  Ophthalmometer  of  Javal  and  Schioetz  62 

39.  Images  of  the  Mires  Seen  Doubled  63 

40.  Eefraetion  by  a  Conical  Cornea  65 

41.  Badii  of  Curvature  of  the  Cornea  67 

42.  Diagram  of  Corneal  Eefraction  69 

43.  Forms  of  the  Image  of  a  White  Square  at  Different  Parts  of 

the  Cornea 71 

44.  Keratoscopie  Images  of  an  Astigmatic  Cornea 73 

45.  Keratoseopic  Images  of  an  Astigmatic  Cornea 74 

46.  Keratoscopic  Images  of  a  Case  of  Keratoconus  75 

46a.  Keratoscopic  Image  of  an  Eye  with  a  Large  Angle  a 76 

46&.  Spot  of  Mariotte  of  an  Eye  with  a  Large  Angle  a 76 

47.  The  Ophthalmophakometer    77 

48.  The  Images  of  Purkinje  Observed  with  the  Ophthalmophakometer  78 

49.  Position  of  the  Images  of  Purkinje,  the  Lamps  being  Arranged 

Vertically    78 

50.  Position  of  the  Images  of  Purkinje,  the  Lamps  being  Arranged 

Horizontally   79 

51.  Defect  of  Centering;  Alignment  of  the  Images  Impossible 80 

52.  Determining  the  Position  of  an  Internal  Surface  of  the  Eye 81 

53.  Determining  the  Position  of  an  Internal  Surface  of  the  Eye 83 

54.  Calculation  of  the  Size  of  the  Circle  of  Diffusion 88 

55.  Rules  of  the  Optometer  of  Young  90 

56.  Magnification  by  Means  of  the  Stenopaic  Opening   93 

57.  Retinal  Image  in  Myopia  and  Hypermetropia 99 

58.  Principle  of  Badal    101 

59.  Size  of  Retinal  Image  when  the  Focus  of  the  Lens  Coincides  with 

the  Anterior  Focus  of  the  Eye  101 

60.  Distribution  of  the  Anomalies  of  Refraction   103 

61.  Refraction  of  a  Pencil  of  Parallel  Rays  by  a  Spherical  Surface. .  114 

62.  Spherical  Aberration  of  a  Lens 116 

63.  Deformity  of  the  Shadows  of  the  Needles 118 

64.  Experiment  of  Volkmann   120 

65.  Distribution  of  the  Light  of  the  Circle  of  Diffusion 121 

66.  The  Aberroscope    122 

67.  The  Rules  of  the  Optometer  of  Young 122 

68.  The  Appearance  Assumed  by  the  Line  of  the  Optometer  of  Young  123 

69.  Deformity  of  the  Shadows  in  an  Eye  with  Strong  Spherical  Aber- 

ration     126 

70.  Aberration  Over -Corrected  Towards  the  Borders 127 

71.  Aberration  Over-Corrected  Above 127 

72.  Aberration  Over-Corrected  Everywhere    127 

72a.  Stadfeldt's  Instrument  for  Measuring  Aberration  of  the  Crystal- 
line Lens  (Dead)    128 

73.  Achromatic  Prism 132 

74.  Prism  a  vision  directe  132 

75.  Chromatic  Aberration  of  the  Eye 135 


FIG.  PAOE 

76.  Phenomena  of  Dispersion  136 

77.  Circles  of  Diffusion  and  Focal  Lines  of  a  Regularly  Astigmatic 

System    138 

78.  Focal  Lines  of  a  Regularly  Astigmatic  System  139 

79.  Construction  of  the  Elliptical  Diffusion  Spot 140 

80.  A  Torus    143 

81.  Focal  Line  of  Lens  Placed  Obliquely  144 

82.  Astigmatism  by  Incidence ;   Focal  Lines   144 

83.  Explanation  of  the  Difference  in  Level  (denivellation)* 148 

84.  Keratoscopic  Images  of  a  Case  of  Keratoconus 157 

85.  Forms  Under  which  a  Luminous  Point  is  Seen  by  a  Regular  Eye  166 

86.  In  Regular  Astigmatism  with  Spherical  Aberration  167 

87.  Figures  of  a  Luminous  Point  Obtained  by  Combining  a  Spheri- 

cal with  a  Cylindrical  Lens   168 

88.  Forms  which  a  Luminous  Point  Presents  to  the  Author's  Right 

Eye    168 

89.  To  an  Eye  with  Double  Obliquity  169 

90.  Figures  of  the  Left  Eye  of  M.  Ree  169 

91.  Curved  Focal  Line   170 

92.  Irregular  Eye   (Diplopia)    171 

93.  Aberroscopic  Phenomena   173 

94.  Diagram  of  Variations  of  Refraction  in  the  Pupil 173 

95.  Course  of  the  Rays  in  the  Author 's  Right  Eye 174 

96.  Specks  on  the  Anterior  Surface  of  the  Cornea 177 

97.  Striae  Produced  by  Winking  177 

98.  Prismatic  Effect  of  the  Layer  of  Tears 177 

99.  Speckled  Appearance  of  the  Entoptic  Field  Produced  by  Rubbing 

the  Cornea   178 

100.     Star  Figure  of  the  Crystalline  Lens 178 

301.     Incipient  Cataract  Seen  Entoptically   179 

lOlo.  The  Entoptoscope 180 

102.     Parallax  of  the  Entoptic  Phenomena 181 

303.    Determination  of  the  Position  of  an  Entoptic  Object 182 

104.  Entoptic  Luminous  Image  Surrounded  by  a  Shadow 183 

105.  Entoptic  Observation  of  the  Vessels    184 

106.  Entoptic  Observation  of  the  Vessels  186 

106a.   Entoptic  Phenomenon    190 

107.  Centripetal  Movement  of  the  Catoptric  Image 196 

108.  Putting  the  Eye  Under  Water  202 

109.  Ciliary  Muscle  of  Man  204 

110.  Ciliary  Part  of  the  Eye  of  a  Cat 205 

111.  Change  of  Aberroscopic  Phenomena  During  Accommodation 206 


*[This  figure  83  does  not  quite  illustrate  the  actual  picture  that  we  obtain  by  looking  at  the 
corneal  images  K  and  L  with  the  ophthalmometer.  For  with  the  Wallaston  prism  K  is  not  seen  any 
more,  but  instead  of  it  we  observe  K,  at  the  place  indicated  in  the  figure,  and  K8  at  a  distance, 
K  K,  to  the  left  of  K  in  the  direction  of  doubling  of  the  prism.  The  same  is  the  case  with  L,,  only 
that  L,  is  displaced  to  the  right.  But  to  avoid  complication  the  two  images  K2  and  L2  have  been 
omitted.]  W. 


FIG. 

112.  Appearance  of  the  Luminous  Point 207 

113.  Appearance  of  the  Luminous  Point  208 

113a.  Skiascopic  Examination  of  Accommodation  210 

114.  Eeflection  Images  of  the  Eye  211 

115.  Eeflection  Images  of  the  Eye 212 

116.  Eeflection  Images  of  the  Eye 212 

117.  Deformity  of  the  Corneal  Image  of  a  White  Square  in  a  Case 

of  Keratoconus   213 

3 18.     Eef raction  by  a  Parabolic  Surface   214 

119.  Deformity  of  the  Crystalline  Surfaces  During  Accommodation..  .  215 

120.  Accommodative  Phenomena  of  the  Eye  216 

121.  Accommodative  Phenomena  of  the  Eye  217 

122.  Change  of  the  Anterior  Chamber  During  Accommodation 219 

122a.  Eeflection  Images  on  the  Anterior  Surfaces  of  the  Dead  Crystal- 
line Lens    220 

122ft.  The  Dead  Crystalline  Lens  and  the  Accommodated  Crystalline 

Lens    221 

123.  Crystalline  Lens  of  the  Ox  223 

124.  Optic  System  of  the  Eye  of  the  Ox 224 

325.     Illumination  of  the  Fundus  by  a  Light  for  which  the  Eye  is 

Accommodated 229 

126.  Illumination  of  the  Fundus  by  a  Light  for  which  the  Eye  is  Not 

Accommodated    230 

127.  Principle  of  the  Ophthalmoscope  of  Helmholtz 231 

128.  Magnification  of  the  Fundus,  both  Patient  and  Observer  being 

Emmetropic    234 

329.    Line  of  Image  of  Papilla  if  the  Fundus  of  Patient  is  Placed  Free 

in  the  Air    235 

130.  Magnification  of  Fundus  if  Patient  is  Myopic 235 

131.  Construction  of  the  Ophthalmoseopic  Field   236 

132.  Magnification  by  the  Inverted  Image  in  Emmetropia 241 

333.     Influence  of  Eefraction  of  the  Examined,  Eye  on  the  Magnifica- 
tion if  Focus  of  Lens  Coincides  with  Anterior  Focus  of  Eye  242 

134.  Influence  of  Eefraction  of  the  Examined  Eye  on  the  Magnifica- 

tion if  Lens  is  Nearer  to  the  Eye  than  in  Fig.  133 243 

135.  Construction  of  the  Ophthalmoseopic  Field  by  the  Inverted  Image  244 

136.  Skiascopy.     Plane  Mirror   247 

3  37.     Skiascopy.     Concave  Mirror   247 

138.  Boundaries  of  the  Skiascopic  Field 249 

139.  Theory  of  Leroy 250 

140.  Theory  of  Leroy   250 

141.  Theory  of  the  Paracentral  Shadow 251 

142.  The  Advantage  of  the  Position  of  the  Pupil  Near  the  Nodal 

Point   .  259 


no.  PAGE 

143.  Experiment  of  Helmholtz    260 

144.  Hyperbolic  Chessboard  of  Helmholtz  261 

145.  Artificial  Eye   262 

146.  Image  of  a  Window  in  the  Artificial  Eye 263 

146a.  Section  of  the  Ketina  of  a  Frog 268 

147.  Experiment  of  Bouger    271 

148.  Curve  Showing  the  Relation  between  the  Light  Sense  and  the 

Illumination    273 

149.  Photoptometer  of  Foerster   275 

150.  Disc  of  Masson   276 

150a.  Disc  of  Helmholtz  and  Disc  of  Benham  277 

151.  Spectrum  of  Refraction;  Spectrum  of  Diffraction  283 

152.  Table  of  Colors  after  Newton 285 

153.  Experiment  of  Ragona  Seina  288 

154.  Experiment  with  Colored  Shadows    289 

155.  Disc  of  Masson   290 

156.  Curves  of  Parinaud  to  Show  the  Threshold  for  Different  Rays  of 

the  Spectrum  296 

157.  Color  Box  of  Maxwell   299 

158.  Mixture  of  Colors  by  Means  of  a  Glass  Plate 300 

159.  Table  of  Colors  after  Newton  303 

160.  Color  Table  of  Maxwell  304 

161.  "Color  Box"  of  Maxwell  305 

162.  Color  Curves  of  Maxwell 306 

163.  Color  Table  of  Maxwell 308 

164.  Color  Table  of  Helmholtz   313 

165.  Color  Table  of  Maxwell 319 

166.  Color  Curves  of  a  Dichromatic   321 

167.  Color  Table  of  a  Dichromatic   321 

168.  Chromatoptometer  of  Chibret   326 

1.69.    Experiment  of  Hooke  335 

170.  Measurement  of  the  Visual  Acuity  by  a  Grating 335 

171.  Measurement  of  the  Visual  Acuity  by  a  Grating  335 

172.  Experiment  of  Hooke,  the  Optics  of  the  Eye  being  Defective 336 

173.  Mariotte's  Blind  Spot   343 

174.  Phenomenon   of  Troxler    344 

175.  Determination  of  the  Center  of  Rotation  of  the  Eye 347 

176.  The  Two  Axes  of  Rotation  Lying  in  the  Horizontal  Plane 347 

177.  Demonstration  of  the  Law  of  Listing 350 

178.  Demonstration  of  the  Law  of  Listing 351 

179.  Demonstration  of  the  Law  of  Listing 352 

180.  Discs  of  Volkmann  356 

181.  Modification  of  the  Experiment  of  Meissner  357 


FIG.  PAGE 

182.  Illustration  of  the  Meter  Angle   364 

183.  Explanation  of  Binocular  Physiologic  Diplopia   370 

184.  Experiment  to  Find  the  Center  of  Projection  373 

185.  Horopter  of  Johannes  Muller  374 

186.  Apparent  Form  of  the  Sky 379 

187.  Influence  of  Parallax  for  Stereoscopic  Vision 380 

188.  Principle  of  Stereoscopic  Images   383 

189.  Stereoscope  of  Wheatstone   385 

190.  Pseudoscope  of  Wheatstone 386 

191.  Telestereoscope  of  Helmholtz   387 

192.  Binocular   Ophthalmoscope    388 

193.  Antagonism  of  the  Visual  Fields 390 

194.  Suppression  of  one  of  the  Images  in  Stereoscopic  Vision 394 

395  to  201.     Optic  Illusions. 


PHYSIOLOGIC  OPTICS 


BOOK  I 

OCULAR  DIOPTRICS 


CHAPTER  I 

OPTIC  PRINCIPLES 

1.  Optic  Properties  of  Bodies. — Bodies  are  of  three  kinds; 
transparent  bodies,  through  which  we  can  see  objects,  translucent 
bodies  such  as  ground  glass,  through  which  we  perceive  light, 
but  cannot  distinguish  form,  and  opaque  bodies. — No  body  is 
absolutely  transparent.  Pure  water  is  transparent,  but  very  little 
light  will  pass  through  a  great  thickness  of  water. — On  the 
contrary  very  thin  layers  of  opaque  substances  are  more  or  less 
translucent,  as  all  know  who  have  examined  microscopic  pre- 
parations. 


*>; 

- — -— . j 

Fig.  1. — A,  luminous  source;  B,  opaque  body;   C,  shadow;  D,  penumbra. 

2.  Rectilinear  Propagation  of  Light. — In  a  homogeneous  me- 
dium light  is  propagated  along  straight  lines  which  are  called 
luminous  rays. 

SHADOWS. — When  rays  emanating  from  a  luminous  point  fall 
upon  an  opaque  body  there  is  produced  behind  the  latter  a  shadow 
which  is  conical  in  shape.  We  can  construct  the  form  of  this 
shadow  by  drawing  straight  lines  joining  the  different  points  of 

l 


PHYSIOLOGIC  OPTICS 


the  border  of  the  body  with  the  luminous  point.  If,  instead  of  a 
point,  the  source  is  a  luminous  surface  the  shadow  is  surrounded 
by  a  penumbra,  the  intensity  of  which  diminishes  more  and 
more  towards  the  periphery.  An  observer  placed  in  the  shadow 
C  could  not  see  any  point  of  the  luminous  surface ;  placed  in  thfe 
penumbra  D  he  would  see  a  part  of  that  surface,  greater  in  pro- 
portion as  he  approaches  the  border. 

IMAGES  PRODUCED  BY  A  SMALL  APERTURE. — Rays  passing 
through  a  small  aperture  into  a  dark  room  form  on  a  screen  an 
inverted  image  of  exterior  objects.  By  diminishing  the  aperture 
the  image  gains  in  distinctness,  but  loses  in  luminosity.  Photo- 
graphs may  be  taken  in  this  way. 

3.  Reflection   and   Absorption. — Rays   which    strike   the   sur- 
face of  an  opaque  object  are  partly  absorbed  and  partly  reflected. 
If  the  surface  is  not  polished  the  rays  are  reflected  in  a  diffuse 
manner:  each  point  of  the  surface  sends  back  light  in  all  di- 
rections.    It  is  through  the  agency  of  this  irregularly  reflected 
light  that  objects  are  visible,  and  the  fact  that  they  are  visible, 
whatever  may  be  the  position  of  the  observer,  provided  the  rays 
are  not  intercepted,  proves  conclusively  that  any  point  whatever 
of  the  surface  sends  rays  in  all  directions. 

4.  Regular  Reflection. — The  more  polished  the  surface  the  less 
diffuse  is  the  reflection.    Thus  the  surface  of  a  highly  polished 
mirror  is  but  slightly  visible.     Polished   surfaces   reflect   rays 
regularly  following  a  law  which  was  known  from  remote  ages, 
viz.,  that  the  reflected  ray  is  in  the  same  plane  with  the  incident 
ray  and  the  normal  to  the  point  of  incidence,  and  that  both  rays 
form  equal  angles  with  the  normal,  which  is  expressed  by  saying 
that  the  angle  of  incidence  and  the  angle  of  reflection  are  equal. 

The  effect  of  this  reflection  is  to  produce  images  of  external 
objects.  The  image  of  a  point  is  the  place  where  the  rays  which 
emanated  from  that  point  meet  again  after  reflection  or  refrac- 
tion. In  order  that  the  image  may  be  perfect,  all  the  rays  em- 
ployed should  meet  in  a  point.  Generally  this  condition  is  not 
quite  fulfilled,  there  being  more  or  less  pronounced  aberrations. 


OPTIC  PRINCIPLES  3 

— A  point  and  the  image  of  this  point  we  designate  as  conjugate 
points. — An  image  is  real  when  the  rays  proceeding  from  a 
point  meet  again  in  a  point;  it  is  virtual  when  it  is  formed  not 
by  the  reunion  of  the  rays  themselves,  but  of  their  prolonga- 
tions.— A  real  image  can  be  received  on  a  screen ;  a  virtual  image 
cannot,  but  it  is  visible  to  the  eye  which  is  in  the  path  of  the 
rays  because  the  optic  system  of  the  eye  forms  a  real  image  of  it 
on  the  retina,  exactly  as  if  the  virtual  image  was  an  object. 

5.  Plane  Mirrors.  Construction  of  the  Image. — Let  fall  from  a 
point  A  (fig.  2)  of  the  object  a  perpendicular  AB  on  the  sur- 
face, DE,  of  the  mirror,  and  mark  on  its  prolongation  a  point 


*    A 

Fig.  2. — Eeflection  on  a  plane  mirror.  A,  the  object; 
A',  its  image;  DE,  the  mirror;  AC,  incident  ray; 
CF,  reflected  ray. 

A'  so  that  AB  is  equal  to  A'B.  A'  is  the  image  of  A,  for  since 
AB=A'B,  the  two  angles  a  are  equal,  and  consequently  also  the 
two  angles  i,  each  of  which  is  equal  90° —  a.  The  image  formed 
by  a  plane  mirror  is  virtual,  erect  and  equal  in  size  to  the  object. 

To  tell  whether  a  mirror  is  true  place  the  eye  near  the  surface 
by  way  of  observing  images  under  as  great  an  incidence  as 
possible.  If  the  mirror  is  not  true  the  images  of  external  ob- 
jects are  deformed.  One  can  also  notice  these  deformities  very 


4  PHYSIOLOGIC  OPTICS 

distinctly  by  placing  oneself  quite  a  distance  in  front  of  the 
mirror  and  observing  the  images  of  distant  objects. 

6.  Concave  Spherical  Mirrors.  —  The  middle  of  the  spherical 
surface  is  called  the  apex,  a  straight  line  passing  through  the 
center  and  the  apex  is  the  axis,  and  the  angular  measurement  of 
the  mirror  is  the  aperture.  In  order  that  images  may  be  true  the 
aperture  must  be  small  (8  to  9  degrees).  The  principal  focus 
of  the  mirror  is  the  place  where  incident  rays  parallel  to  the  axis 
meet  after  reflection.  The  principal  focal  distance  is  the  distance 
of  the  principal  focus  from  the  mirror. 

IN  ALL  OPTIC  PHENOMENA  THE  COURSE  OF  THE  RAYS  is  RE- 
VERSIBLE. —  If  in  figure  2,  the  ray  AC  is  reflected'  along  CF,  an 
incident  ray  along  FC  is  reflected  along  CA.  —  It  follows  that 
rays  coming  from  the  principal  focus  of  a  concave  mirror  must 
be  parallel  after  reflection. 

The  principal  focus  of  a  plane  mirror  is  at  infinity,  because 
incident  parallel  rays  are  still  parallel  after  reflection. 

The  principal  focus  of  a  concave  mirror  is  situated  half  way 

between  the  apex  and  cen- 
ter. We  have,  indeed  i=i 
(fig.  3),  since  the  angles  of 
incidence  and  reflection  are 
equal,  and  i=BC&  because 
the  incident  ray  is  parallel  to 
the  axis.  It  follows  that  C$ 

—  B$,  but  as  the  aperture  is 
Fig.  3.  —  Eeflection  on  a  concave  mirror. 

C,  the  center;  *,  the  focus.  Vel7  small,  we  can  consider 

B^rrrQS),    therefore    C<&= 
=  JL,  if  we  designate  the  radius  by  R. 


A  ray  passing  through  the  center  is  perpendicular  to  the  sur- 
face; it  is  consequently  reflected  on  itself. 

CONSTRUCTION  OF  THE  IMAGE.  —  To  find  the  image  Bx  of  a 
point  B  (fig.  4),  it  suffices  to  trace  the  course  of  two  rays  which 
have  emanated  from  that  point;  the  image  must  be  at  the  place 
where  they  intersect  after  reflection.  After  what  has  been  pre- 


OPTIC  PRINCIPLES 


viously  stated  we  already  know  the  course  of  three  rays  pro- 
ceeding from  the  point  B. 

i°.  The  ray  BM,  which  is  parallel  to  the  axis,  passes  after 
reflection  through  the  focus  <£; 


Fig.  4.  —  Reflection  on  a  concave  mirror.    Constructions  of  the  image,  I,  of 
an  object  O;  C,  the  center;  *,  the  focus.    AS=/i,  A'S=/2, 


2°.  The  ray  B<£,  which  passes  through  the  focus,  is  reflected 
parallel  to  the  axis  since  the  course  of  the  rays  is  reversible; 

3°.  The  ray  BC,  passing  through  the  center,  is  reflected  on 
itself. 


6  PHYSIOLOGIC  OPTICS 

Two  of  these  rays  suffice  for  the  construction.  By  combining 
them,  two  by  two,  we  obtain  the  three  different  constructions 
shown  in  figure  4. 

SIZE  OF  THE  IMAGE.  RELATIONS  BETWEEN  THE  DISTANCES  OF 
CONJUGATE  POINTS. — Let  us  consider  the  line  BA=O  (fig.  40) 
as  the  object;  I  is  its  image.  And  supposing  SL=I  and  MS= 
O,  the  triangles  AB$  and  SL<£  on  one  side,  and  the  triangles 
SM$  and  A'B'<I>  on  the  other  give  us  the  relations 

0  v/i       F 

—  ==  —  =  —  or  /i  /2=FF  (Newton}*. 

1  F        /2 


The  formula 


O        /,  O       2£ 

—  =  —  can  also  be  written  —  =  — ; 
IF  I         R 


which  is  the  formula  we  use  later  in  opthalmometry. — As  we 
have  /!=/! — F  and  /2=/2 — F,  the  formula  of  Newton 

lih=FF 
can  also  be  written 

F      F  111 

_  +  _  =  !  or -+-=:- 

/I  /2  fl         f  * 

The  first  of  these  two  formulae  is  that  of  Helmholtz;  and,  as 
we  shall  see,  it  is  altogether  general.  The  second  is  identical  with 
that  of  infinitely  thin  lenses. 

By  construction  or  formula  we  find  that: 

i°.  The  image  of  an  object  placed  beyond  the  center  is  situated 
between  the  center  and  focus.  It  is  real,  inverted  and  diminished; 


(1)   In  this  formula  and  those  which  follow  I  designate  by:  „ 

0,  the  object; 

1,  the  image  ; 

Rj,  the  radius  of  the  first  surface  ; 

Ra,  the  radius  of  the  second  surface ; 

F*,   the   anterior   focal    distance ; 

Fs,  the  posterior  focal  distance  ; 

fp  the  distance  of  the  object  from  the  surface  ; 

fa,  the  distance  of  the  image  from  the  surface ; 

li,  the  distance  of  the  object  from  the  anterior  focus  ; 

72,  the  distance  of  the  image  from  the  posterior  focus  ; 

For  mirrors  and  lenses  surrounded  with  the  same  media  on  both  sides  we  have 


OPTIC  PRINCIPLES  7 

2°.  As  the  course  of  the  rays  is  reversible,  an  object  placed 
between  the  center  and  the  focus  gives  an  image  situated  beyond 
the  center,  and  this  image  is  real,  inverted  and  enlarged; 

3°.  Afi  object  placed  between  the  focus  and  the  mirror  forms 
its  image  behind  the  mirror.  This  image  is  virtual,  erect  and 
enlarged. 

7.  Convex  Mirrors. — As  in  the  case  of  concave  mirrors,  the 
focus  is  placed  at  an  equal  distance  between  the  surface  and 


Fig.  5. — Reflection  on  a  convex  mirror.     Construction  of  the  image. 
C,  the  center;  <£,  the  focus. 

center.  The  construction  (fig.  5)  is  the  same  as  in  the  preceding 
case,  and  the  formulae  also,  but  the  distances  of  the  points 
situated  behind  the  surface  must  be  considered  as  negative;  we 
have  therefore 

l       1  1 


/i      /2  F 

The  image  of  a  real  object  is  always  virtual,  erect  and  di- 
minished; it  is  situated  between  the  surface  and  the  focus. 

i 

8.  Practical  Bemarks. — One  can  tell  whether  a  mirror  is  con- 
vex, concave  or  plane  by  placing  the  eye  near  the  surface.  A 
convex  mirror  forms  a  diminished  image  of  the  eye,  a  concave 
mirror  gives  a  magnified  image  (provided  the  eye  is  between  the 


8  PHYSIOLOGIC  OPTICS 

focus  and  the  mirror.)     The  image  formed  by  a  plane  mirror 
is  the  same  size  as  the  object. 

To  determine  the  focal  distance  of  a  concave  mirror  we  can: 

1.  Form  the  image  of  a  distant  object  on  a  screen:  the  dis- 
tance of  the  mirror  from  the  screen  is  equal  to  the  focal  distance ; 

2.  Place  the  screen  by  the  side  of  a  flame  and  find  the  distance 
from  the  mirror  at  which  the  image  appears  distinct.    The  dis- 
tance of  the  mirror  from  the  flame  is  double  the  focal  distance, 
for  since  the  object  and  image  are,  in  this  case,  at  the  same 
distance  from  the  mirror,  this  distance  is  equal  to  the  radius  of 
the  mirror  or  double  its  focal  distance.    We  determine  the  focal 
distance  of  a  convex  mirror  by  finding  the  position  of  the  screen 
at  which  the  reflex  which  the  mirror  forms  of  a  distant  flame 
has  a  diameter  equal  to  double  the  diameter  of  the  mirror.    The 
distance  of  the  mirror  from  the  screen  is  equal  to  the  focal 
distance,  as  a  simple  geometrical  construction  will  show. — For 
all  small  mirrors  opthalmometric  processes  are  used. 

Concave  mirrors,  like  convex  lenses,  make  rays  converge, 
while  convex  mirrors  make  them  diverge.  For  this  reason  con- 
vex mirrors  are  used  as  opthalmoscopes  when  it  is  desirable  to 
have  a  very  feeble  light. 

A  combination  of  a  plane  mirror  with  a  convex  lens  acts  like 
a  concave  mirror  with  a  focal  distance  equal  to  that  of  the  lens 
or  half  of  it,  according  as  the  light  traverses  the  lens  once  or 
twice  (opthalmoscope  of  Coccius).  A  combination  of  a  plane 
mirror  with  a  concave  lens  acts  like  a  convex  mirror. 

PORTION  OF  MIRRORS  USED. — Except  in  the  case  when  an 
image  is  projected  on  a  screen  it  is  only  a  small  part  of  the 
mirror  that  is  utilized.  We  can  find  this  part  by  constructing 
the  image  I  (fig.  6)  of  the  object  O  and  by  joining  by  straight 
lines  its  margin  with  the  margin  of  the  observer's  pupil.  These 
straight  lines  delimit  the  utilized  portion  of  the  mirror  AB.  We 
could  also  construct  the  imag£  of  the  pupil  and  join  this  image 
to  the  object;  the  result  would  be  the  same. 


OPTIC  PRINCIPLES 


9.  Refraction. — When  a  luminous  ray  strikes  a  polished  sur- 
face separating  two  transparent  media  is  it  divided  into  two,  a 


Fig.  6. — Construction  of  the  utilized  part  AB  of  a  mirror. 

reflected  ray  which  is  thrown  back  into  the  first  medium  and  a 
refracted  ray  which  continues  its  course  in  the  second  (fig.  7). 
The  three  rays  are  in  the  same  plane  which 
contains  also  the  normal  to  the  point  of  in- 
cidence. The  angle  of  reflection  is,  as  we 
have  seen,  equal  to  the  angle  of  incidence, 
but  the  angle  of  refraction  (formed  by  the 
normal  and  the  refracted  ray)  is  different. 
Its  size  is  determined  by  the  law  of  Des- 
cartes (Snellius).  The  ratio  between  the 
sine  of  the  angle  of  incidence  and  the  sine 
of  the  angle  of  refraction  is  constant,  what- 
ever may  be  the  angle  of  incidence,  as  long 
as  two  media  remain  the  same. 


Fig.  7. 


sin 


sin  r 


The  symbol  n  denotes  the  index  of  refraction,  and  the  index 
of  air  is  generally  adopted  as  the  unit.  The  index  of  water  in 
relation  to  air  is  £=1.333,  that  of  glass  in  relation  to  air  is  ap- 
proximately |  =1.5.  The  index  of  glass  in  relation  to  water 


10 


PHYSIOLOGIC  OPTICS 


is,  then,  |-T-|=|,  etc.  In  the  formulae  which  follow  n  de- 
notes the  index  of  the  second  medium  as  compared  with  that 
of  the  first. 

10.  Quantity  of  Reflected  Light.  Total  Reflection.— The  quant- 
ity of  light  regularly  reflected  increases  with  the  angle  of  in- 
cidence, with  the  difference  of  index  between  the  two  media,  and 
lastly  with  the  degree  of  poish  of  the  surface.  In  air  a  highly 
polished  glass  surface  reflects  about  4  per  cent,  of  incident  light, 
if  the  angle  of  incidence  is  negligible.  Good  metallic  mirrors 
reflect  about  two-thirds  of  the  incident  light. 

Total  reflection  takes  place  when  light,  propagated  in  a  dense 
medium,  meets  at  a  large  angle  of  incidence  the  surface  which 
separates  the  dense  medium  from  a  rarer  one, 


Air 


Water 


Fig.  8. — Total  Eeflection. 

Let  AB  (figt.  8)  be  the  surface  separating  the  air  from  the 
water  and  O  a  luminous  point  in  the  water.  QD  is  a  ray  which, 
on  reaching  the  surface,  is  divided  into  two,  DE  which  is  re- 
fracted and  DF  which  is  reflected  and  much  feebler;  the  next 
rays  OG  and  OH  are  equally  divided;  the  emerging  ray  is  al- 
ways more  and  more  refracted  and  loses  more  and  more  in 
intensity,  while  the  reflected  ray  gains  in  intensity;  and  when 
the  angle  of  incidence  reaches  a  certain  size,  the  emergent  ray 


OPTIC  PRINCIPLES 


11 


forms  an  angle  of  90°  with  the  normal,  that  is,  it  glances  along 
the  surface.  We  designate  as  the  critical  angle  the  angle  of  in- 
cidence which  corresponds  with  an  angle  of  refraction  of  90°. 
In  this  case  sin  r=i;  therefore, 


In  our  case  w=3/4,  sin  1—0.75  and  the  critical  angle  is  about 
49°.  //  the  angle  of  incidence  exceeds  the  critical  angle  all  the 
light  is  reflected  (total  reflection)  (OK,  fig.  8). 

If  we  pour  water  into  a  glass  and  try  to  look  obliquely  from 
below  upwards  through  the  surface  of  the  water  this  surface 
appears  like  an  absolutely  opaque  metallic  surface.  No  ray 
coming  from  above  reaches  the  eye 
because  all  are  deflected  towards  the 
bottom  of  the  glass  by  refraction.  If 
we  dip  a  pencil  in  the  water  we  see 
it  mirrored  in  the  surface ;  rays  com- 
ing from  the  pencil  reach  the  eye  after 
total  reflection  at  the  surface  of  the 
water. 

As  this  form  of  reflection  is  the 
most  complete  of  all,  it  is  frequently 
used  in  optic  experiments.  The  most 
usual  application  of  it  is  in  the  rec- 
tangular prism;  looking  perpendicularly  at  one  of  the  faces  we 
see  an  image  of  objects  placed  in  front  of  the  other  face,  formed 
by  total  reflection  on  the  hypothenuse  (fig.  9).  Nor  need  the 
prism  be  rectangular;  a  prism  of  60°  gives  a  like  result;  but  in 
every  case  the  three  faces  must  be  polished. 

11.  Refraction  by  Plates  with  Plane  and  Parallel  Surfaces. 
—The  incident  ray  and  the  emergent  ray  are  parallel,  for  we 
have  r— r  (fig.  10),  since  the  surfaces  are  parallel,  and  conse- 
quently also  i=i.  The  emergent  ray  has  suffered  a  displacement 
towards  the  side  whence  the  light  comes. 


Fig.    9. — Prism    with    total 
reflection. 


12 


PHYSIOLOGIC  OPTICS 


<V12.  Refraction  by  a  Prism. — Seen  through  a  prism  an  object 
seeing  deflected  towards  the  apex  of  the  prism.  The  angle  be- 
tween the  direction  along  which  the  object  is  seen  and  that  in 
which  it  really  is  found  is  called  the  deviation.  If  i  (fig.  n)  is 
the  angle  of  incidence,  ^  the  angle  formed  by  the  emergent  ray 
with  the  normal,  A  the  angle  of  the  prism,  and  d  the  deviation, 
we  have 

d— t-|4i— A 
for 


and 


Fig.  10. — Refraction  by  a  plate  with    Fig.  11. — Refraction  by  a  prism, 
plane  and  parallel  surfaces. 


therefore 


d=i+i!— A. 


The  deviation  is  least  when  i=il9  the  course  of  the  rays  is 
then  symmetrical,  and  we  have: 

A=2r  and  d=:2i— 2r=2i— A. 


OPTIC  PRINCIPLES  13 

In  the  formula 

sin  i=n  sin  r 

we  can  replace  the  sines  by  the  arcs  if  the  latter  are  small  ; 
therefore  and 

i=nr 


d=2nr-A      (  } 


If  the  prism  is  glass,  we  have  n=  f  approximately,  n  —  1  =  4. 
Therefore  the  deviation  produced  by  a  weak  prism  is  equal  to 
half  its  angle. 

13.  Refraction  by  a  Spherical  Surface.  —  Incident  rays  parallel 
to  the  axis  reunite  at  the  posterior  forget  <£2  (fig.  12).  The 


Fig.  12.  —  Befraction  by  a  spherical  surface.     $1,  the  anterior  focus;  $» 
the  posterior  focus;   C,  the  center. 

distance  S<£2  is  known  as  the  posterior  focal  distance;  it  is  ex 
pressed  by 


n  —  1 
for  we  have 


R  sin  (i—r) 

or,  if  the  angles  are  small, 

r**2 r  r      _  .   1 

~RT      i—r  nr — r     n  — 1 


14  PHYSIOLOGIC  OPTICS 

Therefore 

C$2  _    R 


n  —  1 

and 

I      R    = 


—  1  «  —  1' 


After  refraction  the  rays  coming  from  the  anterior  focus 
3>!  are  parallel  to  the  axis.  Its  distance  ^S^Fj  is  called  the 
anterior  focal  distance  and  is  expressed  by 


indeed,  we  find  this  value  by  a  calculation  analogous  to  that  by 
which  we  have  found  the  posterior  focal  distance. 

d—  i  —  r_|_»!  —  r4  or  for  small  angles 

d—nr—  r_pir,—  r4—  (n—  1)    (r_j_r4)  —  (n—  1)    A.]—  W. 

We  note  that 


that  is  to  say: 

i°.  The  difference  between  the  focal  distances  is  equal  to 
the  radius; 

2°.  The  ratio  between  the  focal  distances  is  equal  to  the  ratio 
betiven  the  indices  of  the  corresponding  media. 

3°.  In  fig.  12  we  have 


The  distance  of  the  center  from  the  posterior  focus  is  equal 
to  the  anterior  focal  distance,  and  the  distance  of  the  center  from 
the  anterior  focus  is  equal  to  the  posterior  focal  distance. 


(1)    [The  author  here  derives  this  formula  from  that  for  the  least  deviation. 
It  may  be  derived  in  a  more  general  way  thus : 


OPTIC  PRINCIPLES 


15 


CONSTRUCTION  OF  THE  IMAGE. — To  construct  the  image  of  a 
point  situated  outside  the  axis  we  can  draw: 

i°.  A  ray  passing  through  the  center;  it  is  not  refracted: 

2°.  A  ray  parallel  to  the  axis:  it  is  refracted  towards  the 
posterior  focus; 

3°.  A  ray  passing  through  the  anterior  focus:  after  refraction 
is  parallel  to  the  axis. 

The  point  of  intersection  of  two  of  these  straight  lines  is  the 
image.  There  are  three  possible  constructions,  therefore,  by 
which  we  may  obtain  the  image  of  this  point. 


Tig.  13. — Refraction  by  a  spherical  surface.     Construction  of  the  image. 
C,  the  center;  $1,  the  anterior  focus;  <E»a,  the  posterior  focus;  O,  the 
object;  I,  the  image.     ASzzr/i,  BS=/2,  A3>i=li  B$n=la. 

Fig.  13  shows  the  construction  by  means  of  rays  2°  and  3°. 
The  triangles  DA<^  and  ^SG  and  the  triangles  HM<I>2  and 
<£0BE  being  similar,  we  have  the  same  relation  as  for  the  mirrors 

O  /I       F£ 

~T    "  TT  "~/2~ 
whence  we  deduce  the  two  general  formulas 


/i  h  =  F,  F2  andll+Z-2-  1. 
/I         /2 

The  image  is  real  and  inverted  when  the  object  is  beyond  the 
anterior  focus;  it  is  smaller  than  the  object  if  the  distance  of 
the  latter  from  the  surface  is  greater  than  2F1,  larger  if  the 
distance  is  less  than  2Fr  If  the  object  is  between  the  focus 
and  the  surface,  the  image  is  virtual,  erect  and  enlarged  and 
behind  the  object. 


16 


PHYSIOLOGIC  OPTICS 


If  the  surface  is  concave  the  radius  is  to  be  considered  nega- 
tive. The  focal  distances  then  become  negative:  Fx=  —  ;^ZT  ^2 
=  —  *  R  ,  which  indicates  that  the  anterior  focus  is  situated 

ft  ~-  1  * 

behind  and  the  posterior  focus  in  front  of  the  surface. 

If,  in  this  latter  case,  the  rays  pass  from  a  dense  medium 
(with  index  —  n)  into  a  rarer  medium  (with  index  =  i),  we 
must  in  the  formulae  replace  n  by  —  .  The  focal  distances  then 
become  positive  again:  F1=  ?_*,  F2=  JL.  This  is  what  hap- 

W—J.  71—  —1 

pens  when  rays,  after  having  passed  through  the  first  surface 
of  a  biconvex  surface,  meet  the  second. 

POWER  OF  A  REFRACTING  SURFACE.—  The  refracting  power  of 
a  surface  is  expressed  in  dioptrics  by  the  inverse  of  the  anterior 
focal  distance  measured  in  meters  :  D==  1  =  «  —  1.  (1) 

FI  R 

If  for  example  the  anterior  focal  distance  is  24  millimeters 
(anterior  surface  of  the  cornea)  the  refracting  power  is  D= 
=42  dioptrics. 


_ 


Fig.  14. — Refraction  by  a  parabolic  surface.     A,  luminous  point;   F,  its 
image;  BG,  normal;  BH,  radius  of  curvature. 

(1)  [In  other  words,  we  define  the  refractive  power  of  a  convex  surface  at  a 
certain  point  B  (fig.  14)  as  the  dioptric  power  of  an  infinitely  thin  plano-convex 
lens  obtained  by  cutting  off  a  piece  of  the  refracting  surface  by  a  plane  at  right 
angles  to  the  normal  at  B  and  very  near  to  this  point.  Such  detached  plano- 
convex lens,  surrounded  by  the  first  medium,  has  a  posterior  focal  distance  Fa 
equal  to  the  anterior  focal  distance  F,,  equal  to  R  and  a  refracting  power 

^J: "-*   •     If  tne  surface  is  not  a  sphere  but  a  surface  of  revolution 

F2        FI          R 
of  the  second  degree,  we  must  replace  R  by  the  normal  N  at  the  point  B.]— W. 


OPTIC  PRINCIPLES  17 

REFRACTION  BY  A  SURFACE  OF  REVOLUTION  OF  THF  SECOND 
DEGREE. — If  the  luminous  point  is  on  the  axis,  refraction  at  a 
given  point  B  (fig.  14)  takes  place  in  the  same  manner  as  if  the 
surface  was  replaced  by  a  sphere  drawn  around  the  point  G 
where  the  normal  BG  meets  the  axis.  If  we  designate  as  N  the 
normal  BG,  the  refracting  power  of  the  surface  at  the  point  B 

is  there  fore  D=*y~1. 

We  can  indeed  calculate  the  focal  distances  for  a  surface  of 
revolution  exactly  as  we  have  done  for  the  sphere,  and  we  find 
the  same  expressions  by  replacing)  R  by  N.  It  is  well  to  note 
that  it  is  the  normal  BG  and  not  the  radius  of  curvature  BH 
which  enters  into  the  formulae. — These  remarks  are  of  im- 
portance for  the  theory  of  accommodation  and  of  keratoconus. 


14.  Infinitely  Thin  lenses. — The  theory  of  lenses  is  very  simple 
if  we  can  neglect  the  thickness.  We  designate  as  axis  the 
straight  line  which  joins  the  two  centers  of  the  surfaces,  and  as 
optic  center  the  point  where  this  axis  crosses  the  lens.  This 
point  enjoys  this  property  that  a  ray  passing  through  it  crosses 
the  lens  without  deviation. 


FOCAL  DISTANCE  OF  A  BICONVEX  LENS.  —  Let  us  designate  the 
radii  of  curvature  of  the  two  surfaces  as  Rj  and  R2.  Incident 
parallel  rays  which  meet  the  first  surface  are  refracted  towards 
the  posterior  focus,  the  distance  of  which,  as  we  have  seen,  is 
equal  to  *_*^  .  .  This  point  now  acts  as  the  object  for  the  second 
surface  ;  as  it  is  behind  the  latter  its  distance  is  to  be  considered 
as  negative.  In  the  formula 


/1  is  therefore  equal  to  —  ^L       Fx  has  the  value  of  -^-^  and 
F2  of  _£L-  (§13).    We  have  therefore 


18 


PHYSIOLOGIC  OPTICS 


—  n—  1 


or 


R2  _j_      R2 
—  "RT    (n  — 1)/2=1 


The  posterior  focus  of  the  lens  is  deduced,  therefore,  from  the 
expression 


The  anterior  focal  distance  is  equal  to  the  posterior  focal  dis- 
tance, for  it  is  clear  that  on  rotating  the  lens  the  expression  _L 
remains  the  same.  We  must  replace  Rx  by  R2,  and  vice  versa, 
which  does  not  change  the  expression. 

CONSTRUCTION  OF  THE  IMAGE  (fig.  15).  —  To  construct  the 
image  A'  of  a  point  A  we  can  draw  : 

i°.  The  ray  AC  passing  through  the  optic  center:  this  ray 
suffers  no  deviation; 

2°.  The  ray  AD  parallel  to  the  axis:  after  refraction  this  ray 
passes  through  <f>2  ; 

3°.  The  ray  A^1  passing  through  the  anterior  focus:  after 
refraction  this  ray  is  parallel  to  the  axis. 


Fig.  15. — Construction  of  the  image  formed  by  a  thin  lens.    BC=/i,  B'C: 
fa,    C* 


OPTIC  PRINCIPLES  19 

These  three  rays  intersect  at  the  point  A,  but  two  suffice  to  find 
this  point. 

The  triangles  AB^  and  S^CE  on  one  side,  and  the  triangles 
DC$>2  and  <J>2B'A'  on  the  other  give  us,  as  in  the  case  of  the 
mirrors,  the  relations: 

_2_=A=   F 
I  F        -7-  or  /i  k=  F2 

/2 

which  can  also  be  written 

JL+J^ior.!-*1  =   1 

/I    ^  *  fl         /2  F    • 

By  the  formula  or  by  construction  we  find  the  following  re- 
lations between  object  and  image: 

1.  If  the  object  is  beyond  the  focus,  the  image  is  real  and 
inverted,  and  on  the  other  side  of  the  lens.     It  is  enlarged  if 
the  distance  of  the  object  from  the  lens  is  less  than  double  the 
focal  distance,  diminished  in  the  contrary  case.    If  the  distance 
of  the  object  from  the  lens  is  equal  to  double  the  focal  distance, 
the  object  and  image  are  of  the  same  size. 

2.  If  the  object  is  between  the  focus  and  the  lens,  the  image 
is  virtual,  erect  and  enlarged;  it  is  on  the  same  side  of  the  lens 
as  the  object,  but  farther  away. 

If,  after  having  placed  a  strong  lens  on  a  printed  sheet,  we 
withdraw  it  gradually  from  the  sheet,  looking  through  it  at 
some  distance  we  see  at  first  an  erect  image  which  is  virtual 
and  situated  back  of  the  lens  and  which  increases  in  size  the 
farther  we  remove  the  latter,  until  the  sheet  is  at  the  focus;  at 
that  moment  the  image  disappears  (it  becomes  so  large  that  a 
single  point  fills  the  entire  field  of  the  lens).  Withdrawing  the 
lens  still  farther  we  see  an  inverted  image  situated  between  the 
lens  and  the  eye.  It  is  enlarged  at  first,  but  rapidly  diminishes 
according  as  the  lens  is  removed. 

CONCAVE  LENSES. — While  biconvex  lenses  and  plano-convex 
lenses,  which  act  in  the  same  manner,  make  incident  rays  con- 
verge, concave  lenses  make  them  diverge.  The  formula  of  the 


20  PHYSIOLOGIC  OPTICS 

focal  distance  remains  the  same,  but  as  the  surfaces  are  concave 
the  radii  must  be  considered  as  negative: 


The  focal  distance  is  therefore  negative  also,  that  is  to  say 
the  focus  is  on  the  side  from  which  the  rays  come.  Incident 
parallel  rays  continue  their  course  as  if  they  come  from  the 
focus  situated  on  the  same  side  as  the  object. 

The  construction  of  the  image  is  analogous  to  that  which  we 
have  employed  for  biconvex  lenses.  It  gives  us  the  same  rela- 
tions as  before  with  the  necessary  changes  of  the  signs: 


O         —  F          /2  /i  — /2         —  F  • 

As  long  as  the  object  is  real,  the  image  is  virtual,  erect  and 
smaller.  It  is  at  the  focus  when  the  object  is  at  infinity.  Ac- 
cording as  the  latter  approaches  the  lens,  the  image  does  like- 
wise, (i) 

MENISCI. — A  lens,  one  surface  of  which  is  convex  and  the 
other  concave,  is  called  a  meniscus.  According  as  the  radius 
of  the  convex  surface  or  that  of  the  concave  surface  is  smaller 
the  meniscus  is  convergent  or  divergent  (positive  or  negative). 
The  positive  meniscus  is  thicker  in  the  middle,  the  negative  is 
thicker  towards  the  edges.  These  rules  are  valid,  however,  only 
when  the  thickness  is  negligible,  which  often  does  not  happen. 

METHODS  OF  MEASURING  THE  FOCAL  DISTANCE  OF  A  LENS. — 
The  method  most  frequently  employed  by  oculists  consists  in 
looking  at  exterior  objects  through  the  lens,  subjecting  the 
latter  to  slight  displacements.  We  then  notice  that  exterior 
objects  are  displaced  in  the  same  direction  as  the  lens  if  the 
latter  is  concave,  in  the  contrary  direction  if  it  is  convex.  In 
other  words,  if  the  eye  is  in  front  of  the  middle  of  the  lens  the 
rays  reach  it  without  any  deviation;  but  if  the  eye  is  placed  be- 


(1)    Generally  the  object  and  image  move  in  the  same  direction   in  all  cases 
of  refraction,  in  an  opposite  direction  in  cases  of  reflection. 


OPTIC  PRINCIPLES 


21 


fore  a  peripheral  part  of  the  lens  it  receives  rays  deflected  by 
reason  of  the  prismatic  effect  of  the  glass,  and  this  effect  is 
greater  in  proportion  as  the  part  throug|h  which  the  eye  looks 
approaches  the  periphery  (fig.  16). — To  determine  the  focal 
distance  of  a  lens  we  find  in  the  test  case  the  glass  which 
neutralizes  it  (i). 


L\ 


Fig.   16. 


But  we  must  remember  that  the  numeration  of  the  glasses  in 
the  test  case  is  frequently  not  very  exact. — Lenses  have  the 
same  curvature  on  both  sides;  we  have  therefore  _i_=2  (*^-i). 
the  index  of  the  lens  is  approximately  w— 1.5,  which  means  that 
the  focal  distance  and  the  radius  are  nearly  the  same  length 
(~~  =  2  (i^-i)  ^^_j  — jt  was  customary  for  a  long  time  to 
number  lenses  according  to  their  radius  of  curvature;  as  the 
index  is  generally  a  little  more  than  1.5,  it  would  follow  that  the 
strong  lenses  would  have  a  focal  distance  somewhat  less  than 
the  number  they  bear,  but  in  the  case  of  convex  glasses  the 
error  would  be  nearly  compensated  for  by  the  influence  of  the 
thickness  of  the  glass. 

Later,  numeration  by  dioptrics   (2)   was  introduced;  and  to 

(1)  We  can  also  use  with  advantage  the  American  sphere-meter,  a  little  instru- 
ment with   which   we  measure   the   radius   of   curvature   and   thus    indirectly   the 
refracting    power    of    the    glass. 

(2)  [In  1872  Monoyer,  of  France,  first  proposed  the  term  "dioptric."     He  says 
in  the  Annales  d'Oculistique,  Vol.  68,  page  111 :     "C'est  le  pouvoir  dioptrique  de 
la  lentille  d'un  metre  ou  100  centimetres  de  longueur  focale  qui  doit  servir  d'unite. 
Cette  unite  nous  I'appellerons  unite  metrique  ou  decimale  de  refraction  ou  simple- 
ment — DJOPTRIE — si   Von  veut   oiens  nous  permettre   ce  neologisme  derive  con- 
iormement   aux  usages  scientifiques.     This   term   has   been   adopted   all   over   the 
world  and  in  English  can  have  only  one  philologically  correct  translation,  that  is 
dioptry.     This  correct  form  has  been  employed,   instead  of  diopter,    all   through 
this   work.] — W. 


22  PHYSIOLOGIC  OPTICS 

obviate  the  necessity  of  changing  the  moulds  in  which  glasses 
are  ground  the  manufacturers  simply  wrote  the  numbers  in 
dioptrics  on  such  of  the  old  lenses  as  most  nearly  corresponded 
with  such  numbers.  It  is  only  recently  that  lenses  have  been 
manufactured  strictly  according  to  the  dioptric  series. 

For  all  these  reasons  it  may  be  useful  for  an  oculist  to  be  able 
to  determine  the  focal  distance  directly.  For  convex  lenses  we 
need  only  form  the  image  of  a  distant  object  on  a  screen.  The 
distance  of  the  lens  from  the  screen  is  the  focal  distance.  —  For 
the  concave  lenses  we  place  a  flame  at  a  great  distance  so  that 
it  forms  its  virtual  image  at  the  focus  of  the  lens  ;  we  then  place 
a  screen  behind  the  latter  and  find  the  position  to  give  to  it  in 
order  that  the  luminous  circle  formed  by  the  lens  would  have  a 
diameter  equal  to  double  that  of  the  lens.  The  distance  of  the 
latter  from  the  screen  is  the  equal  to  the  focal  distance. 

We  can  determine  the  radii  of  curvature  by  means  of  reflec- 
tion images,  by  following  the  formulae  which  we  have  given  for 
the  mirrors.  Knowing  the  radii  and  focal  distance  we  can  cal- 
culate the  index  by  the  formula  -1_  =  («—  i)  (  J_  -u  JL\ 

F  VRl  R2/* 

REFRACTING  POWER  OF  A  LENS.—  The  refracting  power  (D) 
of  a  lens  is  expressed  in  dioptrics  by  the  inverse  of  the  focal 
distance  measured  in  meters: 


We  can  better  realize  the  meaning  of  this  expression  if  we 
recall  the  fact  that  we  expressed  the  refracting  power  of  a 
surface  by  the  inverse  of  the  anterior  focal  distance,  *~1>  The 
refracting  power  of  an  infinitely  thin  lens  is,  therefore,  simply 
the  sum  of  the  refracting  powers  of  its  two  surfaces. 

The  refracting  power  of  an  optical  system  composed  of  sev- 
eral infinitely  thin  lenses  placed  very  near  one  another  is  equal 
to  the  sum  of  the  powers  of  the  lenses. 


OPTIC  PRINCIPLES  23 

15.  Theory  of  Gauss.— If  the  lenses  are  not  so  thin  that  their 
thickness  can  be  neglected,  nor  placed  so  near  one  another  that 
we  can  neglect  their  distances,  we  can  find  the  position  and  size 
of  the  image  by  construction  or  by  calculation  by  the  rules  which 
we  have  given  for  refraction  by  spherical  surfaces :  we  construct 
or  calculate  in  the  first  place  the  image  formed  by  the  first  sur- 
face ;  this  image  then  serves  as  the  object  for  the  second  surface 
and  so  forth.  But  it  is  much  simpler  to  use  the  theory  of  Gauss. 
We  will  briefly  explain  the  essential  points  of  this  theory,  which 
is  applicable  to  every  optical  system  composed  of  spherical  sur- 
faces, supposing  that  the  system  be  centered,  that  is  to  say  that 
all  the  centers  of  the  surfaces  are  on  the  axis  and  that  the 
aperture  of  the  surfaces  is  small. 

According  to  the  theory  of  Gauss,  every  optic  system  has 
six  cardinal  points,  namely : 

Two  principal  points,  ht,  h2  (fig.  17)  ; 

Two  nodal  points,  Kt,  K2 ; 

One  anterior  focus,  ^ ; 

One  posterior  focus,  4>2. 

The  anterior  focal  distance,  Fl=$1  hlt  is  the  distance  of  the 
anterior  focus  from  the  first  principal  point;  it  is  equal  to  the 
distance  of  the  second  nodal  point  from  the  posterior  focus, 
K2*, 

The  posterior  focal  distance,  F2=/^2<I>2,  is  the  distance  of  the 
second  principal  point  from  the  posterior  focus;  it  is  equal  to 
the  distance  of  the  anterior  focus  from  the  first  nodal  point, 
*i  Kr 


A*      Ki  Ka 


Iff.    17. 


Fig, 

It  follows  that  the  distance  of  the  first  principal  point  from 
the  first  nodal  point  is  equal  to  the  distance  of  the  second  prin- 


PHYSIOLOGIC  OPTICS 


cipal  point  from  the  second  nodal  point  and  to  the  difference 
between  the  focal  distances  F2 — Fr  The  distance  between  the 
two  principal  points  is  equal  to  the  distance  between  the  two 
nodal  points. 

The  ratio  between  the  focal  distances  is  equal  to  the  ratio 
between  the  indices  of  the  first  and  last  medium  Zi  =«. 

We  call  principal  planes  two  planes  perpendicular  to  the  axis 
and  passing  through  the  two  principal:  points.  The  image  of  an 
object  situated  in  the  first  principal  plane  is  formed  in  the 
second  principal  plane  and  vice  versa.  It  is  the  same  size  as  the 
object  and  its  direction  is  the  same  as  that  of  the  object. 

A  ray  which,  in  the  first  medium,  passes  through  the  first 
nodal  point,  passes,  after  refraction,  through  the  second  nodal 
point,  and  the  directions  of  the  ray  before  and  after  refraction 
are  parallel. 

Knowing  the  position  of  the  cardinal  points,  the  image  of  a 
given  point  can  be  found  by  construction  or  calculation  in  a 
manner  analogous  to  that  which  we  have  already  employed  in 
the  case  of  infinitely  thin  lenses.  To  find  the  image  of  the  point 
G  (fig.  18)  by  construction  we  can  choose  two  of  the  three 
following  rays : 


¥« 


Fig.  18.  —  Construction  of  the  image  I  of  the  object  O.    L$i= 


i°.  The  ray  GA,  which  is  parallel  to  the  axis,  must  cut  the 
second  principal  plane  at  D,  at  a  distance  from  the  axis  equal 
to  Ahlf  and  it  must  pass  through  3>2.  Its  direction  is  therefore 
DH. 


OPTIC  PRINCIPLES 


25 


2°. The  ray  GB,  which  passes  through  the  anterior  focus  &v 
must,  after  refraction,  be  parallel  to  the  axis :  It  will  then  take 
the  direction  EH. 


3°.  The  ray  GKj,  directed  towards  the  first  nodal  point,  takes, 
after  refraction,  the  direction  K2  H,  parallel  to  its  first  direction. 

The  triangles  GL^>X  and  B/^^  on  one  side  and  the  triangles 
Dh2&.2  and  HM<£2  on  the  other  give  the  relation. 


O  =  A  =  F2 
T     "K      ~h 


We  have,  therefore,  as  before  /^r^ 


and  we  can  deduce 
f1    is 


the   other   general    formula  JA  4.  H.  —  I.  —  Note    that 
reckoned  as  Fl  from  the  first  principal  point,  /2  on  the  contrary 
from  the  second  principal  point. 


Fig.  19. — Construction  to  find  the  second  principal  plane. 


METHODS  OF  FINDING  THE  CARDINAL  POINTS  OF  A  GIVEN 
SYSTEM. — a.  CONSTRUCTION  (fig.  19). — W<e  draw  an  incident  ray 
parallel  to  the  axis  and  we  construct  its  course  by  the  law  of 


26  PHYSIOLOGIC  OPTICS 

Descartes  or  by  the  formulae  which  we  have  given  for  refraction 
by  spherical  surfaces.  We  thus  find  the  posterior  focus.  We 
then  prolong  the  incident  and  emergent  rays;  their  point  of  in- 
tersection is  situated  in  the  second  principal  plane,  and  the  per- 
pendicular let  fall  from  this  point  on  the  axis  marks  the  second 
principal  point  h2.  Repeating  the  same  construction  with  a 
ray  parallel  to  the  axis,  coming  from  the  other  side,  we  find  in 
the  same  manner  the  anterior  focus  and  the  first  principal  point. 
Knowing  these  four  points  we  can  deduce  the  positon  of  the 
nodal  points,  since  the  distance  of  the  first  nodal  point  from  the 
anterior  focus  is  equal  to  the  distance  of  the  second  principal 
point  from  the  posterior  focus,  etc. 

b.  CALCULATION. — Let  us  designate  by  A  and  B  the  two  optic 
systems  which  we  wish  to  combine,  their  focal  distances  by  F\ 
and  F'2  (for  the  system  A)  and  by  F//1  and  F"2  (for  the  system 
B),  and  the  distance  of  the  posterior  focus  of  the  system  A  be- 
hind the  anterior  focus  of  the  system  B,  by  d.  We  can  then 
find  the  cardinal  points  of  the  combined  system  by  means  of 
the  following  formulae  in  which  yl  indicates  the  distance  of  the 
anterior  focus  of  the  combined  system  behind  the  anterior  focus 
of  the  system  A,  and  y2  the  distance  of  the  posterior  focus  of 
the  combined  system  in  front  of  the  posterior  focus  of  the 
system  B. 


The  deduction  of  these  formulae  offers  no  difficulties.  An  in- 
cident ray,  parallel  to  the  axis,  will  pass  after  refraction  by  the 
system  A,  through  its  posterior  focus,  and,  after  refraction  by 
system  B,  through  the  point  $  (fig.  iga)  ;  the  posterior  focus  of 
the  compound  system.  Its  prolongation  meets  the  prolongation 
of  the  incident  ray  at  D  so  that  h2  is  the  second  principal  plane 
of  the  compound  system.  After  the  formula  of  Newton  we  have 


OPTIC  PRINCIPLES 
On  the  other  hand  the  figure  gives  us  the  relations 


F 


F"2) 


,/ 
F 


F'2F" 


tt 


We  find  the  value  of  yl  and  Fx  by  supposing  the  light  to  come 
from  the  other  side.  Knowing  thus  the  focal  distance  and  the 
position  of  the  foci  it  is  easy  to  calculate  those  of  the  other 
cardinal  points. 


& 


Fig.  19a. 

In  the  case  which  the  figure  represents,  d  is  negative,  since 
the  posterior  focus  of  A  is  situated  in  front  of  the  anterior  focus 
of  B;  Fj  and  F2  are,  therefore,  also  negative,  as  well  as  yl 
and  y2 ;  the  compound  system  acts  as  a  concave  lens.  If  d=o 
the  focal  distances  are  infinity:  incident  parallel  rays  are  again 
parallel  after  refraction.  Such  a  system  is  called  telescopic;  a 
telescope  focused  on  infinity  by  an  emmetropic  observer  is  an 
illustration  of  it.  The  distance  d,  the  sign  of  which  determines 


28 


PHYSIOLOGIC  OPTICS 


the  character  of  the  compound  system  is  often  called  the  interval; 
in  the  cases  which  interest  us  it  is  nearly  always  positive. 

SPECIAL  CASES. — As  the  focal  distances  are  proportional  to 
the  indices  of  the  first  and  last  media,  they  ought  to  be  equal 
if  the  first  and  last  media  are  identical,  which  is  true  for  nearly 
all  optical  instruments.  In  this  case  the  distance  of  the  anterior 
focus  from  the  first  principal  point  is  equal  to  its  distance  from 
the  first  nodal  point,  that  is  to  say  the  first  principal  point  coin- 
sides  with  the  first  nodal  point  and  the  second  principal  point 
with  the  second  nodal  point. 

This  is  what  occurs  in  the  case  of  thick  lenses,  in  which  case 
we  can  find  the  nodal  points  by  a  simple  construction.  Let  Cx 
(fig.  20)  be  the  center  of  the  first  surface;  C2  that  of  the  second; 
C2  A  any  radius  whatever  of  the  second  surface,  and  C1  B  a  rad- 
ius of  the  first  surface  parallel  to  C2  A.  Let  us  draw  the  straight 
line  AB,  which  represents  the  course  of  a  ray  in  the  interior  of 

the  lens ;  DB  and  AE 
indicate  its  direction 
outside  the  lens.  It 
is  easy  to  see  that 
these  two  straight 
lines  are  parallel ;  the 
angles  i  are,  in  fact, 
equal,  since  the  an- 
gles r  are  equal.  Pro- 
longing DB  and  AE 
they  cut  the  axis  at 
the  two  points  Kx  and 
K2,  which  are  the 
two  nodal  points. 
The  point  O  is  the 
optic  center  of  the 
lens.  It  is  the  image 

of  K!  in  relation  to  the  first  surface,  and  that  of  K2  in  relation 
to  the  second  surface. 

In  an  infinitely  thin  lens,  the  nodal  points  and  the  principal 
points  all  coincide  with  the  optic  center.  If  the  entire  system 


Fig.  20. — Construction  to  find  the  nodal  points 
of  a  thick  lens. 


OPTIC  PRINCIPLES  29 

is  represented  by  a  simple  refracting  surface,  both  principal 
points  coincide  with  the  surface,  and  the  nodal  points  with 
the  center. 

The  mirrors  may  be  considered  as  dioptric  systems,  in  which 
the  last  medium  has  an  index  equal  to  that  of  the  first  medium, 
but  with  the  contrary  sign,  since  the  rays  run  in  a  contrary  di- 
rection. The  two  principal  points  coincide  with  the  surface,  the 
nodal  points  with  the  center,  and  the  focus  is  at  an  equal  dis- 
tance between  the  two  (since  F^= — F2).  The  compound  re- 
flecting systems  likewise  have  only  one  principal  point  and  one 
nodal  point,  and  the  focus  is  situated  at  an  equal  distance  be- 
tween them.  Such,  for  example,  is  the  case  in  the  compound 
systems  which  give  rise  to  the  images  of  Purkinje  in  the  eye. 

EXAMPLE  i. — To  find  the  cardinal  points  of  the  crystalline  lens. 

Suppose  the  crystalline  lens  has  a  thickness  of  4  millimeters, 
that  the  radius  of  the  anterior  surface  is  10  millimeters  and  that 
of  the  posterior  surface  6  millimeters.  Let  us  take  1.33  as  the 
index  of  the  aqueous  humor  and  the  vitreous  body,  and  suppose 
that  the  index  of  the  crystalline  lens  in  relation  to  these  liquids 
is  about  i. 06. 

In  this  case  each  of  the  systems  A  and  B  is  represented  by  a 
single  refracting  surface.  The  focal  distances  of  the  system 
A  are: 

F'!=      Rl      -    10     ^167*™ 
«— l       006 

F'2=  *«       10  X  i.Q6-mm 


«— 1  0.06 

those  of  the  system  B  are : 

r 

F'  '1=  R2  =      -  6     =6X1.06^1Qfil 
n— 1       1        _i         0.06 
1.06 

-6  X  — 


1.06         1 

The  interval  d  is  the  distance  of  the  posterior  focus  of  the 
system  A  from  the  anterior  focus  of  the  system  B;  the  former 


30  PHYSIOLOGIC  OPTICS 

is  situated  as  177  millimeters  behind  the  anterior  surface,  the 
latter  at  106  millimeters  in,  front  of  the  posterior  surface;  the 
thickness  of  the  crystalline  lens  being  4  millimeters,  we  will 
have  d=i?7  millimeters  +  IQ6  millimeters  —  4  millimeters  = 
279  millimeters,  and 


d  279 

F"i  F",     106  X  100 

—d~         -279 
F       F'!F",        167X106 

—d  -  =       279       =63-4mm 


The  anterior  focus  of  the  crystalline  lens  being  situated  at 
1  06  millimeters  behind  the  anterior  focus  of  the  first  surface  C, 
which  is  at  167  millimeters,  its  distance  as  far  as  that  surface 
will  be  167  —  106=61  millimeters,  and  as  the  focal  distance  is 
63.4  millimeters,  the  first  principal  point  of  the  crystalline  lens 
will  be  placed  at  2.4  millimeters  behind  the  anterior  surface.  The 
second  principal  point  will  be  situated  at  an  equal  distance,  at 
100  —  38-^63.4==:  —  1.4  millimeters,  that  is  to  say,  1.4  millimeters 
in  front  of  the  posterior  surface. 

Both  focal  distances  are  equal,  as  they  must  be,  since  the  sur- 
rounding media  are  alike.  The  refracting  power  of  the  crystal- 
line lens  would  be  with  these  data  _  I  _  =  15-8  D. 

63.4mm 

EXAMPLE  2.  —  Let  us  consider  the  cornea  as  a  simple  refracting 
surface  with  a  radius  of  8  millimeters  surrounded  in  front  by 
air  («==i),  behind  by  the  aqueous  humor  (n=  1.33=!).  The 
distance  of  the  anterior  surface  of  the  cornea  from  the  anterior 
surface  of  the  crystalline  lens  is  3.6  millimeters.  To  combine 
the  cornea  with  the  crystalline  lens  the  cardinal  points  of  which 
we  have  just  found. 

Here  the  cornea  forms  the  system  A.    Its  focal  distances  are  : 


n  —  1 


r=24mm 


OPTIC  PRINCIPLES  31 

The  principal  points  coincide  with  the  surface.  The  focal 
distances  of  the  system  B  are  those  found  above  for  the  crystal- 
line lens. 

The  interval  d  is  the  distance  of  the  anterior  focus  of  the 
crystalline  lens  as  far  as  the  posterior  focus  of  the  cornea:  d= 
61  mm.-{-32  mm.  —  3.6  mm,=894.  With  these  data  we  find 
for  the  entire  optic  system  of  the  eye: 


Fl=2*X68.4=17[0mm 

F      32X63.4^3  7mm 
89.4 


The  following  table  gives  a  general  idea  of  such  an  optic 
system.  By  position  of  a  point  we  mean  the  distance  of  that 
point  behind  the  summit  of  the  cornea. 

Simplified  Eye. 

Index  of  aqueous  humor  and  vitreous  body  .................  1.33 

—  the  crystalline  lens  ...............................   1.41 

Radius  of  curvature  of  the  cornea  .........................        gmm 

—  —      —      anterior  surface  of  the  crystalline  lens  ----  10mm 

—  —      —      posterior  surface  of  the  crystalline  lens  .  .  .  6mm 
Depth  of  the  anterior  chamber  ............................  3.6mm 

Thickness  of  the  crystalline  lens  ..........................  4mm 

Anterior  focal  distance  of  the  cornea  ......................  24mm 

Posterior  focal  distance  of  the  cornea  .....................  32mm 

Focal  distance  of  the  crystalline  lens  ......................  63.4mm 

Position  of  the  anterior  principal  point  of  the  crystalline  lens  6mm 

—  —      posterior  principal  point  of  the  crystalline  lens  6.2mm 
Anterior  focal  distance  of  the  eye  .........................  17mm 

Posterior  focal  distance  of  the  eye  ........................  22.7mm 

Position  of  the  anterior  principal  point  of  the  eye  ......  ____  1.6mm 

—  —  posterior  principal  point  of  the  eye  ...........       1.9mm 

—  —  anterior  nodal  point  of  the  eye  ..............       7.3mm 

—  —  posterior  nodal  point  of  the  eye  ..............     7.6mm 

—  —  anterior  focus  of  the  eye  ...................  —  15.4mm 

—  —  posterior  focus  of  the  eye  ...................  24.6mm 


32  PHYSIOLOGIC  OPTICS 

Bef  racting  power  of  the  cornea 42D. 

—  —      —      crystalline    lens 16D. 

—  —      —      eye 59D. 

We  shall  see  in  the  following  chapter  that  the  data  with  which 
we  have  made  these  calculations  are  not  rigorously  exact; 
nevertheless,  they  give  a  very  close  approximation,  generally 
sufficient  for  our  purpose.  Later  I  shall  have  recourse  more 
than  once  to  this  system,  which  I  call  the  simplified  eye,  to  dis- 
tinguish it  from  the  complete  optic  system  of  which  we  shall 
treat  in  the  following  chapter. 

Bibliography. — Complete  development  of  the  system  of  Gauss  in  the 
introduction  to  the  physiologic  optics  of  Helmholtz. 

Among  the  numerous  treatises  on  geometric  optics,  I  shall  cite: 

Jamin  and  Bouty.  Cours  de  physique  de  I'Ecole  Poly  technique,  1886. — 
Pouillet-Muller.  Lehrbuch  der  Physik  und  Meteorologie,  8th  edition. 
Braunschweig,  1872.  Of  an  easy  study. — Wullner  (Ad.).  Lehrmuch  der 
ExperimentalphysiJc.  II.  Leipzig,  1877. — Lorenz  (L.).  Die  Lehre  vom 
Lieht.  Leipzig,  1877. 

Among  the  more  complete  works,  but  of  a  more  difficult  study,  we  shall 
cite: 

Verdet  (E.).  CKuvres.  Paris  1872.— Herschel  (Sir  J.  F.  W.).  Light. 
London,  1845.  In  French  by  Verhulst  (P.  F.)  and  Quetelet  (A.).  Paris, 
1829. — Health  (B.  S.).  A  Treatise  on  Geometric  Optics.  Cambridge,  1877. 
— Gariel  (G.  H.).  Etudes  d'  optique  geometrique.  Paris,  1889. 

The  beautiful  works  of  E.  Ab~be  resulted  in  considerable  progress  in 
geometric  optics  during  the  last  twenty  years.  We  will  find  an  account  of 
them  in  Czapski  (S.),  Theorie  der  optischen  Instrumente,  Breslau,  1893, 
and,  in  a  more  easily  accessible  form,  in  the  new  edition  of  Pouillet-Muller, 
by  Pfaundler  (L.)  and  Lummer  (O.),  Braunschweig,  1897. 


CHAPTER  II. 

THE  OPTIC  SYSTEM  OF  THE  EYE 

16.  Optic  Constants  of  the  Eye. — By  means  of  the  theory  of 
Gauss  we  can  calculate  the  cardinal  points  of  any  optic  system 
if  we  know  the  position  and  curvature  of  the  surfaces  and  the 
index  of  the  media.  To  calculate  the  optic  system  of  the  eye 


Fig.  21. — The  optic  system  of  the  eye  (left),  Ci,  Ca,  Cs,  €4,  the  centers  of 
the  four  surfaces  in  their  natural  order;  AB,  optic  axis;  L,  visual  line. 

we  must  know,  therefore,  as  exactly  as  possible  those  numbers 
which  are  frequently  called  the  optic  constants  of  the  eye.  Those 
which  I  have  given  in  the  examples  in  the  preceding  chapter  are 
only  approximate.  The  following  table  gives  the  constants  of 
an  eye,  which  I  have  measured  as  carefully  as  possible  (fig.  21)  : 

Optic  Constants  of  the  Eye. 

Position  of  the  anterior  surface  of  the  cornea 0 

—  —      posterior  surface  of  the  cornea i.lSmm 

—  —      anterior  surface  of  the  crystalline  lens 3.54mm 

—  —      posterior  surface  of  the  crystalline  lens 7.60mm 

Eadius  of  the  anterior  suface  of  the  cornea 7.98mm 

—  —      posterior  surface  of  the  cornea 6.22mm 

—  —      anterior  surface  of  the  crystalline  lens 10.20mm 

—  —      posterior  surface  of  the  crystalline  lens 6.17mm 


Index    of    the    air 

—  —      cornea 

—  —      aqueous  humor 

Total  index  of  the  crystalline  lens. 
Index  of  the  vitreous  body 


>    accepted   < 


1 

1.377 

1.3365 

1.42 

1.3365 


33 


34  PHYSIOLOGIC  OPTICS 

The  positions  and  radii  of  the  surfaces  as  stated  are  according 
to  measurements  which  I  made  by  methods  which  I  shall  men- 
tion later. 

The  only  difference  of  any  importance  between  them  and  those 
found  up  to  the  present  arises  from  the  thickness  of  the  crystal- 
line lens  which,  in  his  schematic  eye  Helmholtz  put  down  as  3.6 
millimeters,  certainly  too  small  a  number  to  be  considered  an 
average.  I  have  also  added  the  numbers  for  the  posterior  sur- 
face of  the  cornea  which  I  was  the  first  to  measure. 

As  to  the  indices  which  cannot  be  measured  directly  on  the 
living  eye  I  have  put  down  1.377  for  the  cornea  after  a  measure- 
ment of  Matthiessen,  which  I  also  have  verified.  Those  of  the 
aqueous  humor  and  vitreous  body  are  very  exactly  known;  we 
can,  indeed,  determine  them  with  great  exactness  by  means  of 
the  refractometer  of  Abbe,  or  by  other  analogous  methods. 

Less  is  known  of  the  index  of  the  crystalline  lens  than  of  the 
other  optic  constants  of  the  eye.  It  must  be  noted  in  the  first 
place  that  this  body  is  not  homogeneous ; 
its  index  gradually  diminishes  starting 
from  the  center  of  the  nucleus  towards 
the  periphery.  The  curvature  of  its 
layers  diminishes  also  towards  the  peri- 
phery, so  that  each  layer  takes  the  form 
of  a  meniscus,  the  concavity  of  which  is 
greater  than  the  convexity.  This  con- 
clusion follows  as  well  from  anatomical 
researches  as  from  optic  observations  Fig.  22.— Optic  system  of 
which  I  made  on  the  eye  of  an  ox  after  the  eye  of  an  ox 

death  (i).  (twice  enlarged-) 

There  is,  indeed,  frequently  produced,  in  the  crystalline  lens, 
after  death,  a  differentiation  between  the  cortical   masses  and 


(1)  The  optic  constants  of  such  an  eye  are  as  follows   (fig.  22)  : 

Radius   of  the   cornea 15  millimeters 

Position  of  the  anterior  surface  of  the  crystalline  lens.  ...      6  

—     posterior  surface  of  the  crystalline  lens...  17 

Radius  of  the  anterior  surface  of  the  crystalline  lens 14          

—  —     posterior  surface  of  the  crystalline  lens...      8          

—  —     anterior  surface  of  the  nucleus 8.5       

—  —     posterior  surface  of  the  nucleus 7  — 


TEE  OPTIC  SYSTEM  OF  TEE  EYE 


35 


the  nucleus,  probably  caused  by  the  imbition  of  water  by  the  su- 
perficial parts.  In  consequence  of  this  process  there  is  produced 
on  the  surfaces  of  the  nucleus  quite  a  regular  reflection,  so  that  in- 
stead of  two  reflection  images  we  see  four  (fig.  23),  when  the 
crystalline  lens  is  exposed  to  the  light  of  a  flame.  Now,  the  posi- 
tion of  these  images  indicates  that  the  curvature  of  the  surfaces  of 
the  nucleus  is  considerably  greater  than  that  of  the  crystalline  sur- 


Fig.  23. — Images  of  Purkinje  of  the  eye  of  an  ox  (dead).  (Flame  of  a 
candle.)  a,  image  of  the  cornea;  fc,  image  of  the  anterior  surface 
of  the  crystalline  lens;  c,  image  of  the  anterior  surface  of  the  nu- 
cleus; d,  image  of  the  posterior  surface  of  the  nucleus;  e,  image  of 
the  posterior  surface  of  the  crystalline  lens. 


faces.    Dr.  Demicheri  has  recently  described  cases  of  alterations 
o'f  the  human  cyrstalline  lens  in  which  we  can  also  observe  four 


36 


PHYSIOLOGIC  OPTICS 


crystalline  images;  their  position  also  indicates  a  greater  curva- 
ture of  the  surfaces  of  the  nucleus  (fig.  24). 


Fig.  24. — Double  crystalline  images  in  cases  of  ' '  false  lenticonus. ' '    After 

Demicheri. 

A.  Looking  straight  in  front. 

a,  image  of  the  cornea;  b,  image  of  the  anterior  surface  of  the 
crystalline  lens;  c,  image  of  the  anterior  surface  of  the  nucleus;  d,  image 
of  the  posterior  surface  of  the  crystalline  lens,  which  coincides,  for  this 
direction  of  the  look,  with  that  of  the  posterior  suface  of  nucleus. 

B.  Looking  outwards. 

a.  image  of  the  cornea;  ft,  image  of  the  posterior  surface  of  the 
crystalline  lens;  c,  image  of  the  posterior  surface  of  the  nucleus. 

It  has  long  been  known  that,  as  a  result  of  this  peculiar  con- 
struction of  the  crystalline  lens,  its  total  index,  that  is  to  say, 
the  index  of  an  imaginary  lens  having  the  same 
form  and  the  same  focal  distance  as  the  crystal- 
line lens,  is  greater,  not  only  than  the  mean  index 
of  the  crystalline  layers,  but  even  than  that  of 
the  nucleus. 

To  account  for  this  paradoxical  phenomenon, 
we  may  suppose  the  crystalline  lens  divided  into 
two  parts,  the  nucleus  and  the  cortical  part,  sup- 
posing the  index  uniform  in  each  part,  but  greater 
for  the  nucleus.  On  account  of  its  great  curva- 
ture and  high  index,  the  nucleus  (a  fig.  25)  would 
then  have  a  very  considerable  refracting  power,  which,  how- 
ever, would  be  diminished  by  the  influence  of  the  cortical  layers 


Fig.  25. 


THE  OPTIC  SYSTEM  OF  THE  EYE  37 

which  act  as  two  concave  lenses  (b,  b).  It  is  clear  that  if  the 
index  of  these  layers  were  higher  their  influence  would  be 
greater,  and  the  refracting  power  of  the  whole  crystalline  lens 
would  consequently  be  weaker. 

Thomas  Young  placed  the  index  of  the  center  of  the  nucleus 
at  1.412,,  and  by  calculation  therefrom  he  deduced  1.436  for  the 
total  index.  Later  Listing  gave  1.455  for  the  total  index,  a 
number  adopted  by  Helmholtz,  but  which  is  decidedly  too  high. 
For  his  new  schematic  eye  this  latter  author  later  adopted  an 
index  (1.4371)  which  was  nearly  identical  with  that  of  Young. 
More  recently  M&tthiessen  tried  to  determine  the  law  after 
which  the  index  of  the  crystalline  lens  varies  from  the  center 
towards  the  periphery,  and  to  calculate  from  it  the  total  index. 
According  to  him  the  difference  between  the  total  index  and 
that  of  the  superficial  layers  would  be  double  the  difference  be- 
tween the  index  of  the  nucleus  and  that  of  these  cortical  layers. 
He  has  found  1437  as  the  total  index,  and  the  average  of  his 
measurements  of  the  central  index  approaches  very  close  to  the 
figures  of  Young. — Measurements  which  I  have  taken  after  a 
new  method,  in  collaboration  with  Dr.  Stadfeldt  (i),  seem,  how- 
ever, to  show  that  the  law  of  Matthiessen  can  be  considered 
only  as  an  approximation,  and,  on  the  other  hand,  the  observa- 
tions of  those  who  have  operated  on  cataract  seem,  as  we  shall 
see  later,  to  call  for  a  lower  total  index.  Alwaiting  the  result 
of  new  measurements  I  adopt  the  number  1.42. 

Thanks  to  the  special  structure  of  this  organ  the  refracting 
power  of  the  crystalline  lens  is  some  dioptrics  stronger  than  it 
would  have  been  if  its  index  had  been  uniformly  equal  to  that 
of  the  nucleus.  In  comparison)  with  the  total  refraction  of  the 
eye  the  increase  is  not  considerable ;  it  might  easily  have  been 
obtained  by  a  slightly  greater  curvature  of  one  of  the  surfaces. 
The  teleologic  reason  for  this  structure  is  rather  to  be  sought  in 


(1)  According  to  the  measurements  of  Stadfeldt,  which  I  shall  mention  later 
on,  the  mean  index  of  the  crystalline  lens  would  be  1.435,  and  the  refracting 
power  of  the  crystalline  lens  would  be  on  an  average  19  D.  (varying  between  17 
D.  and  24  D.). 


*8  PHYSIOLOGIC  OPTICS 

the  mechanism  of  accommodation.  For,  this  mechanism  would 
be,  as  I  understand  it,  impossible  without  the  two  peculiarities 
which  characterize  the  structure  of  the  crystalline  lens:  the 
increase  of  density  and  the  increase  of  curvature  of  the  layers 
according  as  we  approach  the  center. — Another  advantage  of 
this  structure  of  the  crystalline  lens  consists  in  making  weaker 
the  images  of  the  eye  which  I  call  harmful  (nuisibles),  and 
which  I  shall  mention  farther  on. 

17.  Optic  System  of  the  Eye. — Applying  the  theory  of  Gauss  to 
the  data  which  we  have  just  stated,  we  find  the  following  results : 

A. — Optic  System  of  the  Cornea. 

Position  of  the  first  principal  point —  0.13mm 

—  —      second  principal  point —  0.14mm 

—  —      first   nodal    point 8.08mm 

—  —      second  nodal  point 8.07mm 

—  —      anterior  focus 24.53mm 

—  —      posterior   focus 32.47mm 

Anterior  focal  distance 24.40mm 

Posterior   focal   distance 32.61mm 

Refracting    power 40.98D. 

B. — Optic  System  of  the  Crystalline  Lens. 

Position  of  the  first  nodal  point 5.96mm 

—  —      second  nodal  point 6.14mm 

Focal  distance  of  the  crystalline  lens 62.46mm 

Eef racting    power 16.01D. 

Combining  these   two   systems,   we   find   the   complete   optic 
system  of  the  eye. 

C. — Complete  Optic  System  of  the  Eye. 

Position  of  the  first  principal  point 1.54mm 

—  —      second  principal  point 1.86mm 

—  —      first   nodal   point 7.30mm 

—  —      second   nodal  point 7.62mm 

—  —      anterior    focus — 15.59mm 

—  —      posterior   focus 24.75mm 

Anterior    focal    distance 17.13mm 

Posterior  focal  distance 22.89mm 

Eefracting    power 58.38D. 


THE  OPTIC  SYSTEM  OF  THE  EYE 


39 


Thanks  to  these  data  we  may  eliminate,  so  to  speak,  the  entire 
real  optic  system 
of  the  eye.  In  the 
system  which  we 
have  just  calculat- 
ed we  take  into 
consideration  only 
the  course  of  the 
rays  in  the  air  be 
fore  entering  the 
eye,  and  their 
course  in  the  vitre- 
ous body  after 
emergence  from 
the  crystalline 
lens;  their  course 

between  the  anterior  surface  of  the  cornea  and  the  posterior 
surface  of  the  crystalline  lens  remains  unknown  to  us. 

We  note  that  the  refracting  power  of  the  cornea  is  2.5  times 
greater  than  that  of  the  crystalline  lens.  The  sum  of  their  re- 
fracting power  is  not  far  from  being  equal  to  the  refracting 
power  of  the  eye,  because  the  nodal  points  of  the  cornea  are 
quite  near  those  of  the  crystalline  lens  (i). 

The  following  little  table  shows  the  refracting  power  of  each 
of  the  surfaces: 

Anterior  surface  of  the  cornea -f-47.24  D. 

Posterior  surface  of  the  cornea —  4.73  D. 

Anterior  surface  of  the  crystalline  lens -}-  6.13  D. 

Posterior  surface  of  the  crystalline  lens -{-  9.53  D. 


Fig.   26. — Position   of  the   cardinal  points 
of  the  human  eye  (magnified  four  times). 
hi  ha,  principal  planes;  Ki  Ka,  nodal  points. 


Total -J-58.17  D. 


(1)  The  refracting  power  of  the  eye  would  be  exactly  equal  to  the  sum  of  the 
powers  of  its  component  systems,  if  the  anterior  principal  point  of  the  crystalline 
lens  coincided  with  the  posterior  nodal  point  of  the  cornea,  or  if  we  consider 
the  cornea  as  a  single  refracting  surface,  with  its  center.  In  the  formula  of 
paragraph  15  (page  27). 


we  would  have,  indeed,  in  this  case  d— F^^Fi",  which  gives 
_  F'!F"i  1  _        1  1 


40  PHYSIOLOGIC  OPTICS 

The  posterior  surface  of  the  cornea  has,  up  to  the  present, 
been  neglected  by  authors;  we  see  that  it  has  a  certain  impor- 
tance. Its  value  is  negative  and  almost  as  great  as  that  of  the 
anterior  surface  of  the  crystalline  lens.  We  shall  see  that  it 
seems  to  play  a  part  in  certain  forms  of  astigmatism. 

Nevertheless,  we  commit  only  a  very  small  error  by  neglecting 
it,  that  is  to  say,  by  supposing  that  the  substance  of  the  cornea 
does  not  exist;  the  anterior  surface  simply  separating  the  air 
from  the  aqueous  humor.  By  eliminating  the  negative  influence 
of  the  posterior  surface,  the  total  refraction  of  the  cornea 
should  increase,  but  the  power  of  the  anterior  surface  diminishes 
nearly  as  much,  since  we  replace  the  index  of  the  cornea  by 
the  weaker  index  of  the  aqueous  humor.  In  our  case  we  would, 
by  thus  simplifying  the  matter,  have  found  a  refracting  power 
of  the  cornea  equal  to  42.16  D.  instead  of  40.98  D.,  that  is  to 
say,  we  would  have  committed  an  error  of  1.18  D.  or  about  1/50 
of  the  total  power  of  the  eye. 

The  right  eye,  the  optic  system  of  which  I  have  calculated  (in 
the  horizontal  meridian),  is  the  only  one  of  which  up  to  the 
present  time  we  possess  complete  measurements.  It  is  impor- 
tant to  note  that  it  is  not  to  be  considered  as  an  average.  The 
radius  of  the  cornea  is  two  or  three-tenths  of  a  millimeter  above 
the  average,  and  the  length  of  the  axis  of  the  supposed  em- 
metropic  eye,  which  we  have  found  equal  to  24.75  mm.,  is  prob- 
ably also  a  little  above  the  average.  This  eye  is,  therefore,  to 
be  considered  relatively  large,  the  more  so  as  the  person  to 
whom  it  belongs  is  pretty  tall  in  stature.  A  light  degree  of 
astigmatism  with  the  rule  would  also  act  in  the  same  way.  I 
have  measured  some  other  eyes,  but  not  a  sufficient  number  to 
be  able  to  establish  an  average. 

The  figures  which  I  have  just  given  apply  only  to  the  eye  of 
the  adult.  The  eye  of  the  new-born  child  is  much  smaller  (the 
axis  measures  about  17  mm.  instead  of  24  mm.),  so  that  we 
might  expect  to  see  the  curvature  of  all  the  surfaces  increased 


THE  OPTIC  SYSTEM  OF  THE  EYE  41 

in  the  same  proportion.  This  is  not  so:  according  to  the  con- 
cordant measurements  of  Axenfeldt  and  Holth  the  cornea  of 
the  new-born  child  differs  but  little  from  the  adult  cornea.  This 
latter  varies  as  we  shall  see  between  quite  wide  limits  (40  to  47 
dioptrics)  and  the  values  which  we  find  in  the  new-born  child 
are  near  the  higher  limit. 

Compensation  for  the  diminution  of  the  axis  is  made  by  the 
crystalline  lens.  According  to  the  measurements  of  Stadfeldt 
the  crystalline  lens  of  the  new-born  child  is  as  thick  as  that  of 
the  adult,  but  the  diameter  is  6  mm.  instead  of  8  or  9  mm., 
whence  it  follows  that  the  curvature  of  the  surfaces  is  very 
great.  Following  are  some  figures  according  to  Stadfeldt: 

Radius  Radius 

Ant.  surface.  Post,  surface.  Thickness.     Diameter. 

Adlllt llmm  6mm  3.6mm 

New-born 4.5mm  4mm  3.9mm  6mm 

Supposing  that  the  index  is  the  same  as  in  the  adult,  the 
crystalline  lens  of  the  new-born  child  would,  therefore,  be 
nearly  twice  more  refracting,  and  the  crystalline  refraction  in 
the  latter  would  not  be  very  far  from  being  equal  to  the  corneal 
refraction. 

18.  Aperture  of  the  System. — The  theory  of  Gauss  supposes 
that  the  aperture  of  the  system  is  very  small,  which  is  by  no 
means  the  case  in  the  eye,  and  many  errors  committed  in  ques- 
tions of  ocular  refraction  seem  to  me  due  to  the  fact  that  we  do 
not  sufficiently  take  into  account  the  large  aperture  of  the  sys- 
tem. In  optic  instruments  an  aperture  over  ten  or  twelve  de- 
grees is  scarcely  accepted.  Supposing  that  the  pupil  has  a 
diameter  of  4  millimeters,  the  aperture  of  the  cornea  would  be 
20  degrees;  and  a  pupillary  diameter  of  4  millimeters  is  rather 
insufficient,  for  it  must  not  be  forgoten  that  we  generally  ex- 
amine our  patients  with  a  very  strong  light.  In  the  ordinary 
circumstances  of  life,  the  pupillary  diameter  is  most  frequently 
greater  (5  or  6  millimeters),  whence  results  a  series  of  errors 


42  PHYSIOLOGIC  OPTICS 

which  would  be  still  greater  but  for  the  special  precautions 
taken  to  neutralize  them  in  part. 

We  must  bear  in  mind  that  the  pupil  is  seen  neither  in  its  real 
position  nor  at  its  true  size:  it  appears  moved  forward  and  en- 
larged on  account  of  the  refraction  through  the  cornea.  It  is 
easy  to  determine  its  apparent  place  and  size.  In  our  general 

formula.  —    tll=  i,  we  must  put  the  values  of  the  cornea 

f\     '  ft 
of  the  simplified  eye,  Fj—  24,  F2=$2,  and  the  distance  of  the 

anterior  surface  of  the  crystalline  lens  and  of  the  pupil  from 
the  anterior  surface  of  the  cornea,  /2—  3.6,  and  we  find  /1== 
—  3.04.  And  if  the  real  size  is  4  millimeters,  we  put  in  the 
formula  _L=Ii  the  values 

O  /2 


O—  4mm,    F2=32mm)    Z2:=:3.6mni  —  32mm  =  —  28.4mrn; 

therefore 


28.4 

The  pupil  appears,  therefore,  moved  forward  about  0.5  mm. 
and  enlarged  by  the  same  quantity.  The  iris  appears  at  the 
same  time  swelled  in  front. 

What  we  see  is,  therefore,  a  virtual  image  of  the  iris  and  of 
the  pupil.  We  call  these  images  apparent  iris  and  apparent  pupil. 
They  are  aerial  images.  Rays  which,  in  the  air,  are  directed 
towards  a  point  of  the  apparent  pupil  are,  after  refraction  by 
the  cornea,  directed  towards  the  corresponding  point  of  the 
real  pupil. 

If  we  imagine  the  iris  and  pupil  seen,  through  the  crystalline 
lens,  by  an  eye  located  in  the  vitreous  body,  the  pupil  would  no 
longer  appear  in  its  place,  but  the  displacement  would  be  less; 
it  would  be  seen  nearly  o.i  mm.  farther  back  than  it  is  in 
reality,  and  enlarged  0.2  mm.  Rays  coming  from  a  point  of  the 
real  pupil  would  proceed  in  the  vitreous  body  as  if  they  came 
from  the  corresponding  point  of  the  crystalline  image. 

If  we  had  constructed  the  corneal  image  and  the  crystalline 
image  of  a  point  of  the  pupil,  we  would  then  know  that  a  ray 


THE  OPTIC  SYSTEM  OF  THE  EYE  43 

directed  towards  the  former  would  pass,  after  refraction  by 
the  cornea,  through  the  same  point,  and,  after  refraction  by 
the  crystalline  lens,  through  the  crystalline  image  of  the  point. 
The  apparent  pupil  belongs  therefore  to  the  incident  rays  as 
does  the  first  principal  point  or  the  first  nodal  point,  and  the 
crystalline  image  of  the  pupil  belong  to  the  emergent  rays. 

The  luminous  cone  which  enters  the  eye  is  limited  by  the 
apparent  pupil;  in,  its  course  between  the  cornea  and  the  crys- 
talline lens,  it  is  limited  by  the  real  pupil,  and,  in  the  vitreous 
body,  by  the  crystalline  image  of  the  pupil.  There  are  analogous 
phenomena  in  most  optical  instruments,  wherever  a  diaphragm 
is  between  two  lenses;  Professor  Abbe  has  proposed  the  names 
of  pupil  of  entrance  and  pupil  of  exit  for  the  images  of  the 
diaphragm. 

We  have  seen  that  the  principal  planes  are  each  the  image  of 
the  other,  and  that  they  have  this  characteristic  that  the  object 
and  image  are  of  the  same  size. 

In  the  formula  H   4.  —  =    i.  the  distances  marked   i   are 

f\          ~    /2 

calculated  to  start  from  the  first  principal  point,  those  marked  2 
to  start  from  tte  second  principal  point.  But  in  this 


Fig.  27. — aa,  pupil  of  entrance;  fcfc,  pupil  of  exit;   O,  object;  I,  image; 
*i,  anterior  focus;  $2,  posterior  focus. 

formula  we  can  as  well  calculate  the  distances  from  any  other 
pair  of  points,  one  of  which  is  the  image  of  the  other.  We 
might  measure,  for  example,  from  the  pupil  of  entrance  and 
pupil  of  exit.  We  would  thus  have  in  figure  27  the  relation 
MI_  ,  _M2  .__  j  an(j  we  could  find  the  image  of  an  object  by  con- 

tni  ml 

structions  analogous  to  those  in  which  we  have  used  the  prin- 
cipal planes.  The  only  difference  is  this:  if  an  incident  ray 


44  PHYSIOLOGIC  OPTICS 

meets  the  first  principal  plane  at  a  distance  from  the  axis  equal 
to  y,  the  emergent  ray  also  cuts  the  second  principal  plane  at 
a  distance  from  the  axis  equal  to  3;.  But  if  the  incident  ray 
meets  the  pupil  of  entrance  at  a  distance  from  the  axis  equal 
to  y,  the  emergent  ray  cuts  the  plane  of  the  pupil  of  exit  at  a 
distance  from  the  axis  which  is  to  y  in  the  same  relation  as 
the  diameter  of  the  pupil  of  exit  is  to  that  of  the  pupil  of  en- 
trance. In  our  case  it  would  be  the  relation  of  ff .  This  mode 
of  procedure  is  often  more  convenient  than  the  classic  method, 
more  especially  because  it  is  easy  by  this  construction  to  cal- 
culate the  diameter  of  the  luminous  cone. 

19.  Point  of  Fixation.  Visual  Line. — To  distinguish  an  object 
clearly  it  is  necessary  to  fix  it,  that  is  to  say,  to  place  the  eye 
in  such  a  way  that  its  image  is  formed  on  the  fovea.  The  point 
fixed  and  the  fovea  are  therefore  conjugate  foci.  But  we  would 
be  greatly  deceived  if  we  thought  that  the  entire  fovea  corre- 
sponded with  the  point  of  fixation.  The  anatomical  fovea  has 
an  extent  of  0.2  mm.  to  0.4  mm.  (Henle)  or  of  0.75°  to  1.50°, 
seen  from  the  posterior  nodal  point  (at  16  millimeters  from  the 
retina).  Looking  at  the  sky  the  fovea  would  cover,  therefore, 
a  part  having  two  or  three  times  the  diameter  of  the  moon, 
which  corresponds  to  a  half  degee.  The  point  of  fixation  is 
much  smaller  in  dimension,  for  we  can  readily  tell  whether  we 
fix  the  right  border  or  the  left  border  of  the  moon.  Generally 
when  two  points  closely  approach  each  other  we  can  still  tell 
which  one  is  fixed  as  long  as  we  can  see  that  there  are  two.  It 
was  Javal  who  specially  insisted  on  this  fact,  to  which  he  attri- 
buted great  importance  for  the  theory  of  binocular  vision. 

We  designate  as  the  visual  line  the  ray  which  goes  from  the 
point  fixed  to  the  first  nodal  point,  and  which,  consequently, 
after  refraction,  reaches  the  fovea  as  if  it  came  from  the  second 
nodal  point.  If,  in  the  aphakic  eye,  we  neglect  the  posterior 
surface  of  the  cornea,  the  visual  line  passes  through  the  center 
of  curvature  of  the  anterior  surface;  it  is,  therefore,  perpen- 
dicular to  that  surface.  In  a  normal  eye  it  is  never,  far  from 
being  so,  since  the  nodal  points  are  very  near  the  center  of 


THE  OPTIC  SYSTEM  OF  THE  EYE  45 

curvature  of  the  anterior  surface  of  the  cornea.  The  direction 
of  the  visual  line  does  not  depend  on  the  position  of  the  pupil. 
In  cases  of  pupillary  displacement  it  may  happen  that  the  ray 
which  represents  the  visual  line  does  not  enter  the  eye.  We 
shall  see  later  (page  78)  how  we  may  determine  experimentally 
the  direction  of  the  visual  line  in  the  eye. 

20.  Optic  Axis.  Angle.  a  — An  exact  centering  would  demand 
that  the  four  centers  of  curvature,  or  the  three,  if  we  neglect 
the  posterior  surface  of  the  cornea,  would  be  on  the  same 
straight  line.  The  centering  of  the  eye  is  never  exact,  but  the 
deviations  that  we  can  establish  are  often  small.  In  some  cases 
I  have,  however,  found  defects  of  centering  relatively  large  in 
eyes,  too,  which  functionally  should  be  considered  normal.  The 
defect  which  I  have  most  frequently  met  consists  in  this,  that 
the  center  of  curvature  of  the  cornea  is  situated  (as  much  as 
a  quarter  of  a  millimeter)  below  the  axis  of  the  crystalline  lens. 
— Neglecting  these  deviations  the  optic  system  of  the  eye  may 
be  considered  as  centered  around  a  straight  line  which  is  called 
the  optic  axis  of  the  eye.  The  fovea  not  being  placed  on  this 
line,  it  does  not  coincide  with  the  visual  line;  it  is  directed 
outward  and  downward  from  the  visual  line  and  forms  with  it 
an  angle  of  5°  to  7°,  called  the  angle  a  (fig.  21). — We  shall  see 
later  that  the  anterior  surface  of  the  cornea  is  not  spherical ;  it 
is  flattened  towards  the  periphery  so  that  it  may  be  compared 
to  an  ellipsoid  of  revolution  around  the  long  axis.  Certain 
authors  designate  as  the  angle  a  the  angle  which  the  line  of 
vision  forms  with  that  axis  which  passes  through  the  most 
curved  part  of  the  cornea  (the  summit).  Generally  the  axis  of 
the  cornea  very  nearly  coincides  with  the  optic  axis  of  the  eye, 
so  thai  both  definitions  amount  to  the  same  thing.  But  we  shall 
see  that  the  comparison  of  the  form  of  the  cornea  to  that  of  an 
ellipsoid  is  very  defective.  Hence  it  may  be  better  to  retain  the 
old  definition. 

We  can  compare  the  optic  system  of  the  eye  with  that  of  an 
opera  glass.     If  the  optician,  by  a  defect  of  workmanship,  had 


46  PHYSIOLOGIC  OPTICS 

placed  one  of  the  lenses  a  little  obliquely,  or  if  he  had  placed 
the  middle  of  this  lens  a  litte  outside  the  axis  of  the  instrument, 
this  defect  would  correspond  with  a  defect  in  the  centering  of 
the  eye. — If,  on  the  contrary,  the  observer  looked  a  little 
obliquely  through  the  glass,  the  visual  line  would  form  with  the 
axis  of  the  glass  an  angle  which  would  correspond  with  the 
angle  «. 

21.  Useful  Image. — The  optic  system  of  the  eye  forms  a  di- 
optric image,  real,  inverted  and  diminished.,  which  is  projected 
on  the  retina  as  the  photographic  image  is  formed  on  the  screen 
of  the  dark  chamber.  The  comparison  between  the  eye  and 
the  dark  chamber  dates  from  the  invention  of  this  instrument 
(Porta,  Leonardo  da  Vinci).  But  although  we  had  from  that 
time  all  the  elements  necessary  to  understand  the  construction 
of  the  eye,  there  continued,  however,  to  prevail  much  confusion 
on  this  question,  more  especially  because  people  could  not  be 
brought  to  admit  that  the  image  which  serves  for  vision  was 
inverted.  It  was  Kepler  (1604)  who  first  explained  the  forma- 
tion of  images  in  general  and  was  led  to  suppose  the  existence 
of  an  inverted  image  on  the  retina,  an  image  which  was  later 
demonstrated  by  Schemer  on  an  eye  from  which  he  had  removed 
a  part  of  the  sclera  and  of  the  choroid. — But,  besides  this  image 
which  I  designate  as  the  useful  imagfc,  because  it  serves  for 
vision,  there  is  formed  in  the  eye  a  series  of  other  images  which 
I  have  designated  as  false  images  of  the  eye,  and  which  will 
form  the  subject  of  the  following  chapter: 


Bibliography. —  (Euvres  ophthalmoliques  of  Thomas  Young,  edited  by 
Tscherning,  p.  134-137. — Listing  (J.).  DioptriTc  des  Auges  in  Wagner, 
Handworterbuch  der  Physiologic. — Tscherning  (M.).  Beitrage  zur  Dioptrik 
dcs  Auges  in  Zeitschrift  fur  Psychologic  und  Physiologic  der  Sinnesorgane, 
III,  p.  429. — Matthiessen.  Die  Neuren  Fortschritte  in  unserer  Kentniss 
von  dem  optischen  Baue  des  Auges  der  Wirbelthiere  in  Beitrage  zur  Psy- 
chologic und  Physiologie  der  Sinnesorgane,  dedicated  to  Helmholtz  on  the 
occasion  of  his  70th  anniversary.  Stadfeldt  (A.).  Recherches  sur  I'indice 
total  du  cristallin  humain.  Journal  de  Physiologie  et  Pathologic.  No- 
vember, 1899. 


CHAPTER  III. 
FALSE  IMAGES  OF  THE  EYE 

22.  General  Remarks. — If  we  place  a  flame  at  some  distance 
from  a  lens,  we  notice  on  the  same  side  with  the  light  two  re- 
flected images  of  the  flame,  one  for  each  surface.  Placing  the 
eye  on  the  other  side  of  the  lens  at  some  distance,  we  see  the 
dioptric  image,  which  is  real,  and,  besides,  a  small,  indistinct 


Fig.  28. — Reflections  and  refractions  by  a  lens. 

image  due  to  a  double  reflection  in  the  interior  of  the  lens,  a 
first  reflection  produced  by  the  posterior  surface,  and  a  second 
by  the  anterior  surface  (fig.  28).  The  rays  which  form  this 
latter  image  undergo,  besides,  a  refraction  by  each  surface  of 
the  lens.  The  small  image  is  real;  we  can,  indeed,  receive  it 
on  a  screen  held  near  the  lens. 

The  incident  light  is  thus  divided  into  three  portions:  useful 
light  which  forms  the  dioptric  image  of  which  we  generally 
make  use,  the  light  lost  by  reflection  on  the  surfaces,  and  lastly, 
the  light  reflected  twice,  which  I  call  harmful  (nuisible).  This 

47 


48 


PHYSIOLOGIC  OPTICS 


harmful  light  may,  indeed,  enter  the  eye  which  is  observing  the 
useful  image,  where  it  is  often  a  cause  of  annoyance,  because  it 
does  not  contribute  to  the  formation  of  that  image.  A  simple 
lens  loses  about  8  per  cent,  by  reflection,  and  the  harmful  light 
represents  only  1/500  of  the  incident  light.  In  complicated 
instruments  much  more  of  the  light  is  lost.  In  the  ophthal- 
mometer  of  Javal  and  Schioetz,  the  loss  is  about  33  per  cent. 

In  the  human  eye  we  may  also  distinguish  between  the  useful 
light  which  passes  through  the  surfaces,  the  light  lost  by  reflec- 
tion, and  the  harmful  light,  which,  having  suffered  two  reflec- 
tions, returns  again  towards  the  retina.  But  the  eye  has  this 
peculiarity  that,  of  all  optic  instruments,  it  is  that  which  loses 
least  light  (about  2  per  cent).  The  harmful  light  is  also  re- 
duced to  a  minimum,,  but  feeble  as  it  is,  it  is  visible  nevertheless. 

The  useful  light  forms  the  dioptric  image  which  serves  the 
purpose  of  vision;  the  lost  light  forms  four  false  images  of  the 
first  order,  called  images  of  Purkinje,  one  for  each  surface; 
they  correspond  to  rays  I,  II,  III  and  IV,  fig.  29.  The  harmful 


Fig.  29. — Manner  in  which  a  luminous  ray  is  divided  in  the  eye. 
A,  incident  ray. — I,  II,  III,   IV,  lost  rays  corresponding  to  the   four 
images  of  Purlcinje;  V  and  VI,  harmful  rays  corresponding  to  the  fifth 
and  sixth  image;   VII,  useful  ray. 

light  forms  a  series  of  false  images  of  the  second  order,  of 
which  one  only  is  visible  (rays  V  and  VI,  fig.  29). 

23.  The  Image  of  Purkinje.— These  images  were  described  at 
the  beginning  of  this  century  by  the  scientist  whose  name  they 
bear,  but  one  of  them,  the  second,  was  lost  sight  of  until  I 


FALSE  IMAGES  OF  THE  EYE  49 

described  it  again  some  years  ago.  (i)  The  first  of  these 
images,  that  due  to  the  anterior  surface  of  the  cornea,  is  pro- 
duced by  a  single  reflection,  the  others  are  formed  by  rays, 
which,  after  having  suffered  one  or  several  refractions,  are  at 
first  reflected,  then  undergo  still  other  refractions  before  emerg- 
ing from  the  eye.  The  optic  systems  which  produce  these  images 
are,  therefore,  quite  complicated,  but  we  can  always  replace  them 
by  a  single  reflecting  surface,  which  I  call  the  apparent  surface. 

Suppose,  for  example,  that  we  wish  to  study  the  third  image 
of  Purkinje,  that  produced  by  reflection  at  the  anterior  surface 
of  the  crystalline  lens.  Neglecting  the  weak  refraction  by  the 
posterior  surface  of  the  cornea,  the  rays  suffer,  besides  reflec- 
tion, two  refractions,  one  on  entering  and  the  other  on  emerging 


Pig.  30. — Position  of  the  seven  images  in  the  eye.    The  object  is  supposed 
to  be  situated  at  20  degrees  below  the  visual  line. 

from  the  eye.  Now,  we  can  replace  this  series  of  refractions 
and  reflections  by  a  simple  reflection  on  the  apparent  surface. 
We  find  the  position  of  this  surface  by  finding  the  position  of 
the  image  of  the  real  surface,  seen  through  the  cornea,  in  the 
same  manner  as  we  have  already  found  the  position  of  the  ap- 


(1)   See  Blix,  however.     Oftalmometriska  Studier.     Uppsala,  1880,  p.  63. 


50  PHYSIOLOGIC  OPTICS 

parent  pupil,  by  means  of  the  formula -*l-f—  —  i;  with  the 
values  of  the  simplified  eye  we  have  F1=24  mm.,  F2=32  mm., 
/2— 3.6  mm.,  which  gives  the  position  of  the  apparent  surface, 
/j— — 3  mm.  We  then  find  the  position  of  the  center  of  the 
apparent  surface  by  finding  in  the  same  manner  the  image  of  the 
center  of  the  real  surface  seen  through  the  cornea  (^  =  13.5, 
which  gives  /2— — 17.5).  The  apparent  surface  being  at  3  mm. 
and  its  center  at  17.5  mm.,  it  must  perform  the  function  of  a 
convex  mirror  of  14.5  mm.  radius,  placed  three  millimeters  be- 
hind the  cornea.  The  focus  is  at  an  equal  distance  between  the 
surface  and  the  center,  that  is  to  say  at  10.2  mm.  behind  the 
cornea;  it  is  therefore  very  nearly  at  this  place  that  the  third 
image  of  Purkinje  is  formed.  We  can,  also  use  the  apparent 
surface  to  calculate  the  size  of  the  image,  following  the  formula 
°-=-| (see- page  6). 

To  make  the  same  calculation  for  the  posterior  surface  of  the 
crystalline  lens,  we  must  first  calculate  the  refracting  system 
composed  of  the  cornea  and  of  the  anterior  surface  of  the  crys- 
talline lens,  and  then  the  images  of  the  posterior  surface  and  of 
its  center,  seen  through  this  system. — With  the  exception  of  the 
anterior  surface  of  the  crystalline  lens,  the  apparent  surfaces 
differ  only  slightly  from  the  real  surfaces. 

The  three  first  surfaces  being  convex  their  images  are  erect, 
while  that  of  the  fourth  is  inverted. — The  object  being  generally 
at  quite  a  distance,  the  images  are  formed  very  near  the  catoptric 
foci  of  the  apparent  surfaces.  The  first,  second  and  fourth  are 
nearly  in  the  pupillary  plane,  while  the  third  is  situated  at  7  or 
8  mm.  behind  this  plane  (fig.  30). — Besides,  the  third  image 
easily  disappears  behind  the  iris  when  the  eye  makes  a  slight 
movement,  which  makes  this  image  more  difficult  to  observe 
than  the  others. 


24.  Manner  of  Observing  the  Images  of  Purkinje. — The  first 
image,  that  of  the  anterior  surface  of  the  cornea,  is  much  the 
brightest;  its  observation  offers  no  difficulty. 


FALSE  IMAGES  OF  THE  EYE 


51 


To  observe  the  second  image  we  place  ourselves  as  when  we 
wish  to  examine  a  patient  by  oblique  illumination,  and  we  ex- 
amine the  eye  with  a  magnifying  glass,  a  lens  of  10  D.  for 
example,  but  without  concentrating  the  light  on  the  eye. 

Examining  the  corneal  image  of  the  flame,  we  shall  see  when 
it  approaches  the  border  of  the  pupil,  and  still  better,  when  it 
shall  have  passed  it,  that  it  is  accompanied  by  a  small  image 
which  is  situated  near  it.  The  more  the  images  approach  the 
edge,  the  more  distant  they  are  from  each  other;  near  the  edge 
the  distance  may  exceed  a  millimeter,  and  the  small  one  is  fre- 
quently still  visible  when  the  large  one  has  already  disappeared, 
giving  way  to  the  irregular  reflex  of  the  sclera. 

The  small  image  is  always  situated  between  the  large  image 
and  the  middle  of  the  pupil,  which  indicates  that  the  posterior 
surface  is  more  curved  than  the  anterior  surface.  Suppose, 
indeed,  that  we  used  two  lamps,  one  on  each  side,  and  consider 
the  distance  separating  the  two  lamps  as  the  object  (fig.  31). 


Fig.  31. — Corneal  images  of  two  lamps,  observed  with  the  ophthalmophako- 
meter  The  small  images  beside  the  large  ones  are  due  to  reflection 
by  the  posterior  surface  of  the  cornea. 

It  is  theft  clear  that  the  image  of  the  posterior  surface  is  smaller 
than  that  of  the  anterior  surface,  which  indicates  that  its  curva- 
ture is  greater.  At  the  middle  of  the  pupil  the  small  image  is 
not  visible,  because  it  coincides  with  the  large  one;  they  are, 


52  PHYSIOLOGIC  OPTICS 

indeed,  situated  at  the  same  distance  from  the  summit  of  the 
cornea. 

The  third  image,  the1  largest,  always  preserves,  whatever  we 
may  do,  a  more  or  less  diffuse  appearance,  due  to  the  fact  that 
the  index  varies  in  the  superficial  layers  of  the  crystalline  lens. 
To  observe  it  we  place  ourselves  as  before,  requesting  the  person 
whose  eye  is  being  examined  to  look  in  a  direction  which  nearly 
bisects  the  angular  distance  between  the  eye  of  the  observer 
and  the  flame.  By  moving  his  eye  slightly  from  side  to  side  the 
observer  will  quite  easily  see  the  image  which  presents  itself 
as  a  broad  glow,  pale  and  more  or  less  diffuse,  and  which 
changes  position  at  the  least  movement  of  the  observed  eye. 

After  having  found  the  image,  we  can  concentrate  the  light  on 
the  eye;  by  this  means  we  magnify  the  image,  which  soon  fills 
the  entire  pupil.  If  the  ligjht  is  bright  the  pupil  frequently  ap- 
pears white,  as  if  the  eye  was  affected  by  a  ripe  cataract,  and  we 
may,  by  examining  it  with  the  magnifying  glass,  thus  observe 
anatomical  details  which  we  cannot  discover  in  any  other  way. 
I  recommend  to  clinicians  this  examination,  of  which  I  have 
nowhere  found  a  description.  ( I )  To  make  the  experiment  un- 
der the  best  conditions  we  must  select  a  lens  of  large  aperture, 
place  the  luminous  source  at  quite  a  distance  and  hold  the  lens 
in  such  a  way  that  its  focus  coincides  with  the  catoptric  focus 
of  the  surface. 

The  third  image  is,  as  we  shall  see,  of  great  importance  for 
the  study  of  accommodation. 

The  fourth  image  does  not  generally  offer  any  difficulties  to 
the  observer. — It  is  observed  under  the  same  conditions  as  the 
preceding  one,  by  directing  the  look  of  the  observed  person  a 


(1)  Rings  of  DJSMICHERI. — Demicheri  has  recently  (Bulletin  of  the  Society  of 
Ophthalmology  of  Paris)  described  phenomena  of  coloration  which  are  observed 
by  this  method  in  the  pupil  in  certain  affections  of  the  crystalline  lens.  The 
middle  of  the  pupil  appeared  blackish  blue  ;  it  was  surrounded  by  a  green  zone, 
then  by  a  yellow  zone,  and  lastly  by  a  red  zone,  near  the  pupillary  border.  The 
case  under  consideration  was  one  of  more  or  less  mature  cataract.  In  a  case 
which  I  have  examined,  and  in  which,  moreover,  the  crystalline  lens  appeared 
intact,  the  pupil  was  filled  by  this  examination  with  an  intense  red,  so  that  one 
would  have  thought  it  filled  with  blood. — These  colors  are  probably  phenomena 
of  interference  due  to  the  reflection  on  the  finely  reeded  surface  of  the  crystalline 
mass,  nearly  like  the  colors  which  mother-of-pearl  presents,  but  the  conditions 
under  which  they  are  produced  are  still  unknown. 


FALSE  IMAGES  OF  THE  EYE 


53 


little  towards  the  lamp.    It  is  small  and  distinct.    Being  inverted 
it  moves  in  a  direction  contrary  to  that  of  the  others. 

For  a  more  minute  examination  of  these  images  my  ophthal- 
mophakometer  may  be  used  (fig.  32).  It  is  composed  of  a  smalt 
telescope,  supported  on  a  stand,  and  of  a  copper  arc  movable 
around  the  axis  of  the  telescope,  and  bearing  a  scale,  the  zero 
of  which  coincides  with  this  axis.  The  radius  of  the  arc  is  86 
centimeters.  The  head  of  the  observed  person  is  fixed  by  a 
head-rest  in  such  a  manner  that  the  eye  which  we  are  to  examine 


Fig.  32— The  Ophthalmophakometer. 


is  at  the  center  of  the  arc. — On  the  arc  move  several  cursors, 
which  carry  electric  lamps.  Each  lamp  is  enclosed  in  a  tube 
closed  in  front  by  a  plano-convex  lens,  which  concentrates  the 
light  on  the  observed  eye. — I  will  speak  later  of  the  manner  of 
using  the  instrument  for  measuring  the  internal  surfaces  of  the 
eye. 


54:  PHYSIOLOGIC  OPTICS 

25.  False  Images  of  the  Second  Order. — All  the  reflected  rays 
which  emerge  from  the  eye  to  form  the  images  of  Purkinje, 
with  the  exception  of  those  of  the  first  image,  meet  surfaces 
which  again  reflect  a  part  of  the  light;  this  light  is  extremely 
feeble  for  most  of  the  surfaces;  it  is  only  on  meeting  the  an- 
terior surface  of  the  cornea  that  there  is  reflected  sufficient  light 
to  be  visible.     Thus  there  are   formed  two  more  images,  the 
fifth,  produced  by  a  first  reflection  on  the  anterior  surface  of 
the  crystalline  lens,  and  a  second  reflection  on  the  anterior  sur- 
face of  the  cornea,  and  the  sixth,  due  to  a  first  reflection  on  the 
posterior  surface  of  the  crystalline  lens  and  a  second  reflection 
on  the  anterior  surface  of  the  cornea. — As  the  rays  return  to- 
wards the  retina,  these  images  are  subjective. 

The  optic  systems  which  produce  these  images  are  very  com- 
plicated. They  are  calculated,  too,  by  the  formulae  which  we 
have  explained  on  page  26.  The  focus  of  the  fifth  image  is 
near  the  posterior  surface  of  the  crystalline  lens.  It  is,  there- 
fore, at  this  place  that  this  image  of  a  distant  object  is  formed. 
Before  reaching  the  retina  the  rays  are  so  dispersed  that  they 
are  no  longer  visible ;  I,  at  least,  have  not  been  able  to  discover 
the  least  trace  of  this  image.  Theoretically  we  ought  to  be  able 
to  make  it  visible  by  bringing  the  object  nearer,  since  the  image 
and  object  move  in  the  same  direction  as  in  all  the  refracting 
systems,  but  the  experiment  did  not  succeed.  In  fact,  when  the 
flame  with  which  we  are  working  is  moved  near  enough  to  the 
eye,  the  useful  image  becomes  transformed  into  a  diffusion 
circle,  which  fills  the  greater  part  of  the  field  and  prevents  one's 
seeing  anything  else. 

The  focus  of  the  sixth  system  is,  on  the  contrary,  very  near 
the  retina  of  the  emmetropic  eye;  the  image  is  also  genera. ly 
easy  to  observe. 

26.  Manner  of  Observing  the  Sixth  Image. — We  choose,  in  a 
half-darkened  room,  a  point  of  fixation  situated  some  distance 
away,  and,  having  fixed  this  point,  we  give  to  the  candle,  held 
in  hand,  a  to-and-fro  horizontal  motion,  moving  it  towards  and 
away  from  the  visual  line  without,  however,  reaching  it. 


FALSE  IMAGES  OF  THE  EYE  55 

We,  then,  notice  on  the  other  side  of  the  visual  line  a  pale 
image  of  the  flame.  Some  people  see  the  phenomenon  sufficiently 
distinct  to  be  able  to  discern  that  the  image  appears  inverted, 
the  retinal  image  being  erect.  We  discern  more  clearly  the  form 
of  the  image  when  we  cause  the  candle  to  pass  below  the  visual 
line;  the  image  then  passes  above,  and  we  see  that  its  apex  is 
directed  downwards.  Myopes  see  the  image  with  greater  diffi- 
culty; they  often  succeed  better  when  using  their  correcting 
glasses,  but  they  must  then  guard  against  confounding  it  with 
the  images  produced  by  repeated  reflections  between  the  cornea 
and  the  glasses. 

It  seems  that  there  are  persons  who  cannot  perform  the  ex- 
periment successfully.  If  the  anterior  chamber  is  unusually 
deep  it  may,  indeed,  happen  that  the  focus  of  the  system  is 
quite  a  distance  from  the  retina,  but  we  ought  then  to  be  able 
to  succeed  by  moving  the  flame  towards  the  eye  or  away  from  it. 

We  see,  therefore,  how  very  advisable  it  is  that  the  harmful 
light  be  reduced  to  a  minimum;  in  fact,  if  the  index  of  the 
superficial  crystalline  layers  had  been  higher,  the  sixth  image 
would  have  had  more  brilliancy,  and  we  would  be  affected  with 
an  annoying  monocular  diplopia.  And  right  here  we  must  pause 
to  wonder  at  the  enormous  sensitiveness  of  the  retina,  for  the 

brightness  of  the  sixtfo  image  is  really  only  — 1 of  that  of  the 

useful  image. 

One  can  study  the  sixth  image  more  closely,  by  means  of  the 
opthalmophakometer,  by  placing  oneself  in  the  place  of  the  per- 
son examined,  and  by  fixing  the  middle  of  the  objective  of  the 
telescope,  which  corresponds  to  the  zero  of  the  division. 

Placing  the  arc  horizontally,  and  putting  the  lamp  A  which 
slides  on  the  arc  at  some  distance  from  the  telescope,  we  see 
the  image  appear  on  the  other  side.  We  bring  one  of  the 
cursors  of  the  arc  to  coincide  with  the  image,  so  that  we  may 
read  its  position  on  the  scale.  We,  then,  notice  that  the  image 
is  only  approximately  symmetrical  with  the  lamp,  in  relation 
to  the  visual  line.  By  causing  the  arc  to  rotate  180°  in  such  a 
way  as  to  bring  the  lamp  into  a  position  symmetrical  with  the 


56  PHYSIOLOGIC  OPTICS 

former,  we  notice  that  the  image  no  longer  coincides  with  the 
cursor.  This  is  on  account  of  the  angle  0.  If  the  visual  line 
coincided  with  the  optic  axis,  the  two  positions  of  the  image 
corresponding  to  two  positions  symmetrical  with  the  lamp,  ought 
to  be  symmetrical.  We  can  use  measurements  of  this  kind  to 
determine  the  size  of  the  angle  a. 

It  was  while  using  the  opthalmophakometer  that  I  found  this 
image,  which  I  described  as  new  in  1891.  But  Coccius  had  seen 
it  previously,  and  Otto  Becker  had  given  the  explanation  of  it  in 
1860  in  a  memoir  which  is  very  little  known.  Heuse  described 
it  again  in  1872,  but  gave  an  erroneous  explanation  of  it. 

The  images  of  Purkinje  have  no  interest  as  far  as  the  function 
of  the  eye  is  concerned,  but  they  are  of  great  importance  for 
the  physiology  of  vision.  It  is,  indeed,"  by  a  study  of  them  that 
we  can  determine  the  form  and  position  of  the  refracting  sur- 
faces of  the  eye.  The  study  of  these  images  constitute  opthal- 
mometry,  to  which  we  will  devote  our  attention  in  the  following 
chapter. 

Bibliography. — Purkinje  (I.  E.  Commentatio  de  examine  physiologico 
organi  visus  et  systematic  cutanei.  Vratislavise,  1823. — Becker  (O.).  Ueber 
Wahrnehmung  eines  Reflexbildes  im  eigenen  Auge,  Wiener  medicinische 
Wochenschrift,  1860,  p.  670-672  and  684-688.— Heuse.  Ueber  die  Beobach- 
tung  'einer  neuen  entoptischen  Erscheinung.  Graefe's  Archiv.  Bd.  18,  2, 
p.  236. — M.  Blix.  Oftalmometrislca  Studier.  Upsala,  1880. — Tscherning. 
Eecherches  sur  la  quarieme  image  de  PurMnje;  Arch,  de  physiol.,  1890. — 
Tscherning.  Theorie  des  images  de  PurTcinje  et  description  d'une  nouvelle 
image.  Arch,  de  physiol.,  1891. — Tscherning.  Sur  une  nouvelle  image  a  la 
fois  catoptrique  et  dioptrique  de  I'oeil  humain  et  une  nouvelle  methode  pour 
determiner  la  direction  de  I'axe  optique  de  I'oeil.  Bulletin  de  la  So- 
ciete  francaise  d'ophthalmologie  1891,  p.  203. 


CHAPTER  IV. 
OPHTHALMOMETRY 

27.  Principles  of  Ophthalmometry—  The  basis  of  ophthalmom- 
etry  is  the  formula  °  =  '  =  *  or  R  =  *1  (see  page  6). 

1  r  Jv  O 

To  determine  the  radius  R  of  the  small  convex  mirror  which 
forms  the  anterior  surface  of  the  cornea,  we  measure  the  image 
I  of  an  object  O,  placed  at  a  given  distance  /.  There  is  never 
any  difficulty  measuring  either  the  object  or  the  distance;  it  is, 
therefore,  to  the  measurement  of  the  image  that  we  must  devote 

our  attention. 

f 

We  may  say  at  once  that  we  generally  use  as  objects  the  dis- 
tances separating  two  flames  or  two  white  objects  (mires). 
The  image,  then,  is  the  distance  separating  the  images  of  the 
flames  or  of  the  mires. 

The  method  most  used  by  physicists  for  such  measurements 
consists  in  placing  a  micrometer  at  the  focus  of  the  objective  of 
the  telescope  with  which  the  image  is  observed.  The  objective 
forms  an  image  which  coincides  with  the  micrometer,  the  gradu- 
ations of  which  permit  the  size  of  the  image  to  be  read  directly 
by  observing  it  through  the  eye  piece.  It  has  been  attempted 
to  use  this  method  for  ophthalmometry,  but  without  success. 
As  the  observed  eye  cannot  be  kept  absolutely  quiet,  the  image 
is  constantly  changing  its  place  in  relation  to  the  micrometer, 
which  makes  a  fairly  exact  measurement  impossible. 

This  is  why  Helmholtz  introduced  into  ophthalmometry  an- 
other principle  which  he  borrowed  from  astronomy,  where  the 
same  problem  presents  itself,  that  of  doubling  (dedoublement). 
It  seems,  however,  that  the  method  had  already  been  used  for 
the  same  purpose  by  Thomas  Young. 

Suppose  that  we  desire  to  measure  the  distance  I  separating 
the  two  points  a  and  b  (fig.  33,  i),  and  that  we  have  a  process 
which  permits  us  to  see  everything  doubled  at  a  certain  distance 

57 


58  PHYSIOLOGIC  OPTICS 

D.  By  this  means  instead  of  the  two  points  a  and  b  we  would 
see  four,  at  and  a2,  b±  and  b2,  and  the  distance  at  a2  would  be 
equal  to  bl  b2  and  to  D,  while  the  distance  al  bl^=a2  b2=I 
(fig-  33,  2). 

Suppose,  now,  we  could  make  the  doubling  vary.    By  increas- 
,  ing  it  we  would  reach  a  point 

1-'''  ~~~*  when  a2  and  bt  would  coin- 

cide (fig.  23,3)  which  would 
i__  take    place    at    the    moment 

2         a^C.' -*        J  ?  when  I  would  be  equal  to  D. 

If   we  knew  the  amount  of 
doubling  used  we  would  thus 

j.     ^-.^        __-~~o,  i      have  measured   I=a   b,  and 

our  object  would  be  attained. 
*•  When  a  and  b  touch  we  say 

m  that   we   have   obtained    con- 

*  • 

tact.     If  we  use  as  objects 

•"  separated    flames    so    that    a 

Fig-  33.  and    b    form    two    luminous 

points  we  obtain  more  exact  measurements  by  giving  one  of 
them  the  form  of  two  points  situated  on  the  same  vertical  (fig. 
33,4)  ;  at  the  moment  of  contact  the  image  of  b  is  placed  ex- 
actly between  the  two  points  a.  Instead  of  making  the  doubling 
vary,  we  can  make  I  vary,  which  is  brought  about  by  varying  the 
object  (displacing  one  of  the  lamps)  until  contact  is  obtained. 

Generally  it  is  useful  to  employ  a  certain  degree  of  magnifi- 
cation in  order  to  have  easy  measurements,  and  this  suggests 
the  use  of  a  telescope  placed  at  some  distance  from  the  eye; 
instruments  with  short  focus,  more  or  less  resembling  micro- 
scopes, are  not  practical  because  it  is  impossible  to  keep  them 
in  focus,  the  observed  eye  not  being  able  to  remain  sufficiently 
quiet. 

Thus,  we  would  only  have  to  affix  our  doubling  apparatus  to 
our  telescope  and  place  conveniently  two  flames  or  two  white 
surfaces  which  would  serve  us  as  objects,  and  we  would  be 
ready  to  begin  our  measurements. 


OPHTHALMOMETBY  59 

28.  Methods  of  Doubling  (Dedoublement) . — a)  A  first  method 
consists  in  dividing  the  luminous  cone  which  meets  the  objective, 
into  two  halves,  an  upper  and  a  lower,  and  displacing  each  half 
laterally,  one  to  the  right,  the  other  to  the  left.  We  can  obtain 
this  effect: 

i°.  By  placing  before  the  upper  half  (i)  of  the  objective  a 
weak  prism,  apex  to  the  right,  and  before  the  lower  half  an- 
other, apex  to  the  left. 

2°.  Instead  of  prisms  we  can  use  plane  parallel  plates,  placed 
obliquely  but  in  a  symmetrical  manner  in  relation  to  the  axis 
of  the  telescope.  Such  plates  placed  obliquely  (see  page  12) 
have  the  effect  of  displacing  the  object  laterally,  each  on  its 
own  side;  the  effect  is,  therefore,  the  same  as  that  of  prisms, 
and  the  plates  give  better  images. — This  is  the  system  employed 
by  Helmholtz,  who  made  the  doubling  vary  by  changing  the 
inclination  of  the  plates,  and  later  by  Leroy  and  Dubois,  who 
used  a  constant  doubling  by  making  the  object  vary. 

3°.  We  can  saw  the  objective  in  two  and  displace  the  upper 
half  a  little  to  the  left,  the  lower  half  a  little  to  the  right  (fig. 
34).     It  is  easy  to  see  that  this  method  must  pro- 
duce a  doubling  of  the  image,  since  the  optic  center 

of  the  objective  is,  so  to  speak,  divided  into  two 

V  J  halves,  displaced  laterally  in  relation  to  each  other. 

This  method  gives  very  good  images  and  less  light 
is  lost,  since  we  obviate  the  reflection  on  the  sur- 
faces of  the  prisms  or  plates,  but  the  instrument  is  very  difficult 
to  construct;  the  displacement  of  the  two  halves  of  the  objective, 
in  relation  to  each  other,  must  be  made,  indeed,  with  an  exact- 
ness that  is  expressed  in  hundredth^  of  a  millimeter. 

None  of  these  methods  is  very  practical,  because  all  of  them 
call  for  a  very  exact  adjustment  of  the  instrument  to  find  the 
meridians  of  the  astigmatic  eye  (see  ch.  IXi). — If  the  eye  is  dis- 
placed a  little  during  the  measurement,  we  may  find  false  di- 

(1)  I  am  supposing  here  and  in  what  follows  that  it  is  the  horizontal  meridian 
we  are  measuring. 


60  PHYSIOLOGIC  OPTICS 

rections  for  these  meridians.  Helm-holts  remedied  this  incon- 
venience by  placing  himself  very  far  (at  i  or  2  meters)  from 
the  patient,  which  calls  for  a  room  prepared  for  this  purpose 
and  makes  measurement  pretty  difficult. 

b)  A  second  method  consists  in  dividing  the  objective  into 
two  lateral  halves,  and  displacing  laterally  each  half  of  the 
incident  luminous  cone.  Such  an  arrangement  can  be  obtained: 

i°.  By  placing  in  front  of  the  objective  a  double  prism  with 
apex  vertical  ; 

2°.  By  placing  before  each  half  of  the  objective  a  plate  with 
plane,  parallel  surfaces,  forming  an  angle  with  the  axis  of  the 
telescope  (fig.  35). 

These  are  the  plates  of  Helmholtz  which  are 
placed  side  by  side  instead  of  being  placed  one 
above  the  other. 

3°.  We  can  obtain  the  same  effect  by  removing       FlS-  35- 
a  vertical  band  from  the  middle  of  the  objective  and  cementing 
together  the  remaining  parts  (fig.  36). 

Systems  of  this  order  offer  no  difficulty  in  finding  the  merid- 
ians, but  they  have  another  inconvenience :  contact  depends  much 
on  the  exactness  of  the  adjustment. 
If,  after  having  obtained  contact  the 
observed  eye  is  displaced  a  little,  so 
that  the  instrument  is  no  longer  ex- 
actly in   focus,  contact  ceases.     We 
may  thus  obtain  totally  false  measure-  Fig.  36. 

ments  of  astigmatism  if  the  observed 
eye  is  displaced  between  the  two  measurements. 

This  inconvenience  is  partly  got  rid  of  in  the  model  of  the 
Javal  and  Schivetz  ophthalmometer  which  the  optician  Kagenaar, 
of  Utrecht,  constructed.  It  uses  a  combination  of  the  methods 
b,  i  aqd  b,  2,  a  combination  of  two  very  weak  prisms  forming 
an  angle  between  them ;  the  apex  of  the  prisms  is  inwards. 

r)  The  best  method,  however,  is  to  emloy  doubly-refracting 
crystals.  Coccius  had  recourse  to  a  place  of  spar;  Jatval  and 
SMoetz  used  a  Wollaston  prism.  This  prism  (fig.  37)  is  com- 


OPHTHALMOMETEY 


61 


posed  of  two  rectangular  quartz  prisms,  which  are  cemented 
together  so  as  to  form  a  single  very  thick,  plane  parallel  plate. 

The  two  prisms  are 
cut  differently  in  the 
crystal;  one  has  the 
apex  parallel  to  the 
axis  »of   the   crystal, 
"*^     the  other  perpendic- 
ular to  it.     Each  ray 
""'•-.^  which  passes  through 

NX-^  the  prism  is  divided 

Fig.  37.— Prism  of  Wollaston.  into  two,  and  each  of 

the  two  new  rays  is 

deviated  a  little  so  that  they  are  nearly  symmetrical  in  re- 
lation to  the  incident  ray.  (i) — By  all  other  systems  which  I 
have  mentioned  the  incident  cone  is  divided  into  two  half 
cones,  which  are  a  little  displaced  in  relation  to  each  other;  the 
prism  of  Wlollaston  on  the  contrary  produces  two  entire  cones 
of  half  the  intensity. 

The  instrument  of  Helmholtz  must  be  considered  as  an  in- 
strument for  the  laboratory.  Investigators,  like  Bonders  and 
Mautkner,  used  it  for  measuring  the  eyes  of  some  patients,  but 
its  use  was  so  difficult  that  Mauthner  exclaimed:  "Ophthal- 
mometry  must  be  understood  as  ophthalmoscopy,  only  it  is  much 
more  difficult."  Besides  it  necessitates  a  dark  room,  and  the 
complete  measurement  of  the  cornea  calls  for  not  less  than  32 
measurements.  It  is  only  by  the  labors  of  Javal  and  Schioetz 
that  ophthalmometry  has  become  a  clinical  method. 

29.  The  Ophthalmometer  of  Javal  and  Schioetz. — The  instru- 
ment (fig.  38)  is  composed  of  a  telescope  which  carries  a  copper 
arc  movable  around  the  axis  of  the  telescope,  and  with  a  head- 
rest on  which  the  head  of  the  patient  is  supported;  when  the 


(1)  [A  detailed  theory  of  this  prism,  together  with  a  calculation  of  the  angles, 
can  be  found  in  the  Theorie  de  I'ophtalmomttrie  de  la  cornee  by  Dr.  Tscherning 
in  Javal's  Memoires  d'ophtalmometrie,  Paris  1891.] — W. 


62 


PHYSIOLOGIC  OPTICS 


telescope  is  adjusted  to  the  level  of  the  eye  of  the  observed 
person,  the  latter  is  at  the  center  of  the  arc. — Two  white  mires 


Fig.  38. — Ophthalmometer  of  Javal  and  Schioetz. 

slide  along  the  arc,  and  it  is  the  distance  separating  them  which 
serves  as  the  object.  By  moving  one  of  the  mires  on  the  arc, 
the  size  of  the  object  is  made  to  vary  until  it  corresponds  with 
the  doubling  of  the  prism  which  is  constant. — The  telescope  has 
two  achromatic  objectives  between  which  is  the  Wollaston 
prism,  placed  so  as  to  double  in  a  direction  exactly  parallel  to 
the  plane  of  the  arc.  It  is,  besides,  provided  with  a  Ramsden 
eye  piece  with  a  spider's  thread.  Each  observer  must  begin  by 
focusing  the  ocular  on  the  thread;  then  the  instrument  is  ad- 
justed for  the  level  of  the  observed  eye  by  displacing  it  forwards 
or  backwards.  We  then  see  the  images  of  the  two  mires  doubled 
(fig.  39)?  and  by  displacing  the  mire  on  the  right,  contact  is 
obtained.  This  done  we  can  read  the  distance  of  each  mire  in 


OPHTHALMOMETRY 


63 


degrees  from  the  axis  of  the  telescope  on  the  scale  of  the  arc, 
and  the  sum  of  the  two  figures  indicates  the  corneal  refraction. 
I  have  supposed  the  cornea  in  question  spherical,  otherwise  we 
would  have  to  begin  by  finding  the  principal  meridians;  but  I 
shall  reserve  the  description  of  the  measurement  of  the  astig- 
matic eye  for  the  chapter  on  astigmatism. 

Generally  the 
patient  must  look 
into  the  telescope: 
it  is  only  when  we 
wish  to  measure 
the  peripheral  parts 
of  the  cornea  also 
that  we  make  him 
look  in  other  di- 
rections. 

The  graduation 
of  the  arc  is  in  de- 
grees, but  the 
doubling  is  so 
chosen  that  each 
degree  corresponds 
with  one  dioptry. 
This  calls  for  an  explanation. 

Javal  and  Schioetz  have  taken  as  the  index  of  the  aqueous 
humor  i  .3375  ( i )  ;  the  refracting  power  of  the  cornea  ex- 
pressed in  dioptrics  would  be,  therefore  (see  page  16)  ; 

r>_l        n  —  1      0.3375 


Fig.  39. 


R 


R 


or,  expressing  R  in  millimeters, 


(1)  This  value  of  n,  very  nearly  correct,  was  selected  in  order  that,  in  the 
following  table,  45  D.  would  correspond  exactly  to  7.5  mm.,  which  is  convenient 
in  order  to  regulate  the  instrument  by  a  sphere  type  of  7.5  mm. 


64 


PHYSIOLOGIC  OPTICS 


With  this  formula  we  calculate  the  following  table,  which 
gives  the  relation  between  the  refracting  power  of  the  cornea, 
expressed  in  dioptrics,  and  the  radius  expressed  in  millimeters ; 

Refraction.  Radius.  Refraction.    Radius.     Dioptries.     Radius. 


50  D. 

6.75mm 

45  D. 

7.5mm 

40  D. 

8.44mm 

49  D. 

6.89mm 

44  D. 

7.67mm 

39  D. 

8.65mm 

48  D. 

7.03mm 

43  D. 

7.85mm 

38  D. 

8.89mm 

47  D. 

7.18mm 

42  D. 

8.04mm 

46  D. 

7.34mm 

41  D. 

8.23mm 

Placing  the  value  which  we  have  just  found  for  R  in  the 
formula 


O         21 


we  find 


337.5 


in  which  formula  I  designates  the  image  which,  at  the  moment 
of  contact,  is  equal  to  the  doubling.  Let  us  designate  by  a  the 
linear  length  of  a  degree;  if  this  length  must  correspond  to  one 
dioptry,  the  object  which  corresponds  with  the  image  I  must 
have  the  size  Da,  therefore 


Da- 


2/DI 


or 


a  = 


337.5 
2/1 


337.5 


On  the  other  hand  as  a  must  be  one  degree  long,  we  have 


1° 
360° 


therefore 


and 


360 


—  2.94mm 


OPHTHALMOMETRY 


65 


In  order  that  a  degree  of  the  arc  may  correspond  with  one 
dioptry,  the  doubling  of  the  prism  must  be,  therefore,  2.94  mm. 
This  is  what  has  been  done. 

The  radius  of  the  arc  (/)  has  been  selected  so  that  the  linear 
length  of  a  degree  may  be  6  millimeters  (5  millimeters  in  the 
new  model). 

In  the  last  models  of  the  instrument  certain  details  have  been 
changed,  but  the  principle  remains  the  same. — We  may  add, 
furthermore,  that,  in  order  to  measure  the  As,  one  of  the  mires 
has  a  special  form  "in  steps,"  each  of  which  corresponds  to  one 
dioptry. — A  keratoscopic  disc  enables  us  to  study  the  general 
form  of  the  cornea. 

UTILIZED  PART  OF  THE  CORNEA. — It  is  only  a  very  small  part 
of  the  cornea  that  is  used  for  the  measurement.  Making  the 
construction  in  the  way  indicated  on  page  9  we  see  that  the 
images  of  the  mires  are  formed  by  reflection  on  two  small  parts 
of  the  cornea  situated  about  1.2  mm.  from  the  visual  line. 


Fig.  40. 


Rotating  the  arc  these  two  parts  move  describing  a  concentric 
ring  around  the  visual  line.  This  ring  is  the  only  part  of  the 
cornea  which  sends  light  into  the  objective,  and  consequently 
also  the  only  part  on  which  the  instrument  can  give  information. 
The  parts  situated  outside  or  inside  this  ring  may  have  curva- 
tures quite  different  from  those  indicated  by  the  instrument. 
Suppose,  for  the  moment,  that  we  have  to  do  with  a  conical 


66  PHYSIOLOGIC  OPTICS 

(hyperbolic)  cornea:  what  we  would  measure  would  be  the 
radius  of  BG  of  the  circle  BE  (fig.  40),  which  touches  the  sur- 
face of  the  cornea  at  B  and  E  (see  page  16).  Generally  this 
circle  coincides  quite  closely  with  the  "optic"  part  of  the  cornea ; 
but  if  we  want  to  make  very  exact  measurements  we  must 
always  take  into  consideration  this  source  of  errors. 

EXACTNESS  OF  THE  MEASUREMENTS. — With  a  good  illumina- 
tion an  experienced  observer  would  not  easily  be  led  astray  to 
the  extent  of  a  quarter  of  a  dioptry,  which  corresponds  to  almost 
2*  of  a  millimeter  of  error  for  the  radius.  Absolute  reliance 
cannot,  therefore,  be  placed  in  the  second  decimal  of  the 
measure  of  the  radius.  Donders  and  Hamer  arrived  at  very 
nearly  the  same  results  using  the  ophthalmometer  of  Helmholtz. 
— Still  more  accurate  results  may  be  obtained  by  using  trans- 
lucent mires  which  are  illuminated  from  behind  by  electric 
lamps.  In  these  conditions  an  experienced  observer  can  almost 
guarantee  exactness  to  a  tenth  of  a  dioptry  or  thereabouts. 

30.  Results  of  the  Measurement  of  the  Cornea. — The  radius  of 
the  cornea  (at  the  summit)  varies  between  7  and  8.5  mm.  It 
is  extremely  rare  to  find  a  cornea  the  radius  of  which  is  not 
situated  between  these  limits,  except  in,  cases  of  keratoconus. 

The  cure  (fig.  41)  shows  the  distribution  of  the  different 
curvatures  in  a  certain  number  of  men  (emmetropes)  whom  I 
examined  in  collaboration  with  Dr.  Bourgeois.  The  average 
was  43.1  D=7.8  mm.  It  is  noticeable,  however,  that  these  same 
measurements  show  that  the  radius  is  greater  in  persons  tall  in 
stature  and  with  a  large  cranial  circumference,  (i)  Now  the 
persons  whom  we  examined  were  indeed  of  tall  stature  (cuiras- 
siers). It  may  be,  therefore,  that  the  average  length  of  the 
radius  may  be  slightly  smaller  than  that  which  I  have  just  in- 
dicated.— It  would  be  an  error  to  think  that  one  radius  rather 
than  another  corresponds  with  emmetropia.  As  Javal  says  an 
elephant  and  a  mouse  may  both  be  emmetropic  despite  the  fact 
that  their  corneal  radii  must  necessarily  be  very  different. — It 


(1)   Steiger  has   since  found  a   still  more  manifest  relation  between  the   radii 
of  the  corneas   and  the   distance  between   the   eyes. 


OPHTHALMOMETEY 


67 


seems  that  we  can  express  the  relation  by  saying  that  in  the 
emmetropic  eye  there  exists  a  constant  relation  between  the 
radius  of  curvature  of  the  cornea  and  the  length  of  the  ocular 
axis,  so  that  the  ocular  shell  of  different  emmetropic  eyes  would 
always  be  a  reproduction  of  the  same  type,  a  little  enlarged  or 
a  little  diminished. — The  existence  of  the  myopia  and  hyper- 
metropia  of  curvature  (corneal)  is  not  yet  demonstrated  (2) 
except,  perhaps,  for  certain  cases  of  very  high  hypermetropia 
which  approach  microphthalmia ;  but  their  existence  is  beyond 
doubt. 

If  I  except  cases  of  astigmatism^  different  in  both  eyes,  it  is 
very  rare  to  find  a  difference,  ever  so  slightly  noticeable,  be- 
tween the  corneal  refraction  of  the  two  eyes  of  the  same 
person,  even  in  cases  of  anisometropia.  Amongst  the  cuirassiers 


35 
30 
25 
20 
15 
ID- 
S' 


I 


7.17      7.33        7.49      7.66      7.81        8.02      8.23      8.43mm 

Fig.  41. — The  abscissas  indicate  the  radii  of  curvature  of  the  cornea  in 
millimeters,  the  ordinates  the  number  per  hundred  of  emmetropes  in 
whom  we  meet  the  radius  of  curvature  in  question. 

mentioned  above  there  were  not  more  than  two  per  cent,  who 
showed  a  difference  exceeding  a  half  dioptry  between  the 
two  eyes. 

EXAMINATION  OF  THE  PERIPHERAL  PART  OF  THE  CORNEA. — 


(2)   See,  however,  the  communication  of  Sulzer  to  the  Congress  of  the  French 
Society  of  Ophthalmology,   1896. 


68  PHYSIOLOGIC  OPTICS 

Up  to  the  time  when  Javal  and  Schioetz  made  a  clinical  method 
of  ophthalmometry  there  was  little  known  of  the  form  of  the 
cornea.  The  ophthalmometer  of  Helmholtz  being  too  compli- 
cated to  make  many  measurements,  one  was  limited  to  measur- 
ing three  points  of  a  meridian,  that  which  corresponds  to  the 
visual  line  and  another  at  some  distance  on  either  side.  Ate  the 
peripheral  radii  were  found  to  be  greater  than  the  central  radius, 
and  as,  in  consequence,  the  cornea  could  not  be  considered  as  a 
sphere,  the  curvature  of  the  second  degree  which  approached 
nearest  the  meridian  measured  was  calculated  (see  fig.  42). 
Thus  it  was  that  the  idea  was  disseminated  that  the  form  of 
the  cornea  (non-astigmatic)  would  be  that  of  an  ellipsoid  of 
revolution  around  the  long  axis,  which  axis  would  be  directed 
outwards  from  the  visual  line  and  form  an  angle  of  about 
5°  (a)  with  this  line.  This  idea  differs  widely  from  the  reality; 
the  cornea  does  not  resemble  an  ellipsoid.  Helmholtz  insisted 
from  the  start  on  the  fallacy  of  the  comparison. 

After  the  construction  of  modern  ophthalmometers  it  became 
much  easier  to  study  this  question.  The  second  model  of  the 
Javal  and  Schioetz  ophthalmometer  is  provided  with  a  very  large 
keratoscopic  disc  divided  into  graduations  of  5°  by  concentric 
rings.  After  having  made  the  usual  measurements,  during  which 
time  the  patient  looks  at  the  center  of  the  objective,  the  measure- 
ment is  repeated  making  him  look  5°  to  the  left,  10°  to  the  left, 
etc.;  and,  after  having  thus  measured  the  right  half  of  the 
horizontal  meridian  we  measure  the  left  half.  We  repeat  the 
measurements  for  the  vertical  meridian. — Measurements  of  this 
kind  have  been  made  in  Paris  by  Sulzer  and  Eriksen  (fig.  42)  ; 
these  measurements  confirmed  the  assertion  of  Aubert  and  Mat- 
thiesen  who,  using  the  ophthalmometer  of  Helmholtz,  had  said 
that  the  cornea  could  be  divided  into  two  parts,  a  central  one, 
which  is  approximately  spherical  and  which  we  call  the  optic 
part,  and  a  peripheral  one  or  basilar  part,  which  is  much  flat- 
tened. Eriksen  reckoned  as  belonging  to  the  optic  part  that  part 
the  refraction  of  which  does  not  differ  more  than  one  dioptry 
from  the  central  refraction.  Its  extent  varies  a  little  in  different 


OPHTHALMOMETRY  69 

eyes.     Following  are  the  limits  of  the  optic  part  compared  with 

those  of  the  entire  cornea,  after  Eriksen  : 

Optic  Part.  Cornea. 

Outwards 16.5  °  44.7  ° 

Inwards 14°  40.1  o 

Above 12.5o  38.5° 

Below 13.5o  42.2o 

The  figures  are  the  averages  of  measurements  made  on  24  eyes. 
The  total  width  of  the  cornea  is,  therefore,  not  much  less 


*0°  30°  20°  10°         ti-     0°  10°  20°  30°  Mr 

Visual  Line 

Pig.  42. — Diagram  of  corneal  refraction  after  Eriksen. — The  abscissas  in- 
dicate the  distance  of  the  visual  line  in  degrees,  the  ordinates,  the 
corneal  refraction  in  dioptrics. 

The  full  curve  indicates  the  refraction  of  the  horizontal  meridian  of 
a  left  cornea  measured  in  graduations  of  five  degrees.  The  zero  corresponds 
to  the  visual  line. — aa,  optic  part  of  the  cornea;  oib,  ob,  basilar  part. — The 
dotted  curve  cc  corresponds  to  the  ellipsoid  calculated  according  to  the 
three  measurements  taken  at  0°  and  25  o  on  the  right  and  left  of  the  visual 
line;  dd  is  the  axis  of  this  ellipsoid  and  the  distance  of  this  line  from  zero 
corresponds  to  the  angle  which  is  often  called  the  angle  ». — We  see  that 
the  true  form  of  the  cornea  differs  considerably  from  the  ellipsoid. 


70  PHYSIOLOGIC  OPTICS 

than  90°,  and  that  of  the  optic  part  is  about  30°,  or  a  third  of 
the  entire  width.  The  horizontal  diameter,  as  well  that  of  the 
optic  part  as  that  of  the  entire  cornea,  is  a  little  greater  than 
the  vertical  diameter. 

Neither  Sulzer  nor  Eriksen  have  found  an  axis  of  symmetry 
properly  so  called.  Nevertheless,  most  of  the  diagrams  of  the 
latter  show  a  tendency  to  symmetry  around  an  axis  directed 
about  5°  outwards  and  a  little  below  the  visual  line.  If,  there- 
fore, the  comparison  with  an  ellipsoid  is  persisted  in,  we  must 
imagine  it  much  more  pointed  than  we  have  done  up  to  the 
present,  and  we  must  suppose  the  summit  cut-off  by  a  section 
perpendicular  to  the  axis  and  replaced  by  a  spherical  cap. 

As  far  as  the  optics  of  the  eye  are  concerned,  the  obliquity  of 
the  cornea  plays  only  a  slightly  important  role,  since  the  optic 
part  of  the  cornea  is  nearly  spherical.  This  part  corresponds 
to  a  linear  diameter  of  about  4mm.  When  the  pupil  is  large  the 
basilar  part  may,  therefore,  play  a  certain  part;  according  to 
the  little  table  of  Eriksen  it  would  be  especially  inwards  and 
above  that  its  influence  would  be  felt.  But  it  is  impossible  to 
know  anything  of  it  without  having  examined  each  eye  by 
itself,  for  the  obliquity  of  the  cornea  is  often  compensated  for 
by  the  eccentricity  of  the  pupil.  The  position  of  the  pupil 
varies  much  in  different  eyes.  Sulzer  found  that  on  an  average 
the  center  of  the  pupil  is  5°  outwards  from  the  visual  line,  and 
that  it  is  sometimes  displaced  upwards,  sometimes  downwards. 
This  decentering  of  the  pupil  may,  therefore,  compensate  for 
the  obliquity  of  the  cornea,  so  that  it  is  especially  outwards 
that  we  must  expect  to  notice  the  effect  of  the  peripheral  flatten- 
ing. 

The  basilar  portion  is  less  regular  and  much  less  polished  than 
the  central  portion,  which  partly  explains  the  slight  success'  of 
optic  iridectomies.  The  catoptric  images  have  frequently  a 
diffuse  aspect  and  the  ophthalmometric  measurements  leave  much 
to  be  desired.  Eriksen  also  has  tried  to  obtain  an  idea  of  the 
variation  of  the  radius  of  the  peripheral  parts  by  examining 
the  form  which  the  image  of  a  white  square  assumes  in  the 
horizontal  meridian,  at  different  distances  from  the  visual  line. 


OPHTHALMOMETEY  71 

We  see  on  fig.  43  that  the  image  becomes  longer  and  longer 
until  about  30°  from  the  visual  line,  where  it  is  two  and  a  half 
times  greater  than  at  the  center.  Just  at  the  periphery  the 


Fig.  43. — Forms  of  the  image  of  a  white  square  at  different  parts  of  the 
cornea  (horizontal  meridian,  internal  half),  after  Eriksen. — The 
figures  at  the  top  of  the  squares  indicate  the  distance  in  degrees 
from  the  visual  line;  those  at  the  bottom  the  refraction  (in  the 
horizontal  meridian)  in  dioptrics. 

image  becomes  narrower,  and  ends  as  a  rectangle  placed  upright ; 
at  this  place  the  image  is  sometimes  double;  a  second  image  is 
formed  still  farther  away  on  the  edge  towards  the  sclera,  and 
this  image  is  inverted  in  the  horizontal  direction,  but  not  in 
the  opposite  direction.  These  latter  phenomena  indicate  that 
the  curvature  increases  very  considerably  towards  the  border, 
and  that  beyond  this  place  there  is,  at  least  in  some  eyes,  a 
concavity,  like  a  furrow  which  separates  the  cornea  from  the 
sclera.  We  must  note  that  the  images  should  increase  a  little  in 
height  towards  the  periphery  at  the  same  time  that  they  increase 
in  width,  because  the  curvature  diminishes  also  in  the  vertical, 
but  much  less  than  in  the  horizontal  direction.  This  increase 
is  not  indicated  on  the  figure. 

In  a  general  way  we  may,  therefore,  consider  the  portion  of 
the  cornea  which  plays  a  part  in  the  optics  of  the  eye  as  spheri- 
cal, so  that  the  angle  a,  understood  in  the  sense  in  which  we 
generally  accept  it,  loses  its  importance. — This  is  why  I  have 
defined  the  angle  °  as  being  the  angle  between  the  visual  line 
and  the  optic  axis  of  the  eye,  a  definition  which  others  have  also 
given  to  it. 

Note,  furthermore,  that  the  normal  cornea  is  slightly  astig- 
matic; we  reserve  a  special  chapter  for  this  anomaly  of  re- 
fraction. 


72  PHYSIOLOGIC  OPTICS 

The  radius  of  the  normal  cornea  does  not  fall  below  7  mm., 
but  in  cases  of  keratoconus  we  may  meet  radii  of  6  or  5  mm., 
or  even  still  smaller  radii,  to  a  point  where  the  arc  of  the  oph- 
thalmometer becomes  too  short;  we  cannot  separate  the  mires 
sufficiently  to  obtain  contact.  The  images  of  the  mires  assume 
in  this  case,  as  also  when  there  are  corneal  opacities,  irregular 
forms. 

By  the  Sulzer-Eriksen  method  we  determine  the  radius  of 
curvature  at  a  given  part  of  the  cornea.  We  obtain  by  this 
method  a  :very  good  idea  of  the  form  of  the  cornea,  but  the 
results  are  not  directly  applicable  to  ocular  dioptrics  for  the 
reasons  given  on  page  16.  To  be  able  to  calculate  the  aberration 
produced  by  a  peripheral  flattening  of  the  cornea,  we  should 
know  the  normal  (the  part  of  the  perpendicular  to  the  cornea 
comprised  between  the  latter  and  the  visual  line).  To  deter- 
mine it  Brudzewski  made  certain  changes  in  the  ophthalmometer. 
He  replaced  the  arc  by  a  larger  one,  reaching  170°.  One  of  the 
mires  is  fixed  at  the  middle  of  the  arc  so  that  its  border  when 
prolonged  would  pass  through  the  axis  of  the  telescope,  while 
the  other  mire  slides  on  the  arc  so  as  to  be  able  to  obtain  con- 
tact. The  observed  person  fixes  the  middle  of  the  objective 
during  all  the  measurements.  He  uses  prisms  of  different 
doubling  power.  He  begins,  for  example,  with  a  prism  doubling 
i  mm. ;  and,  the  arc  being  placed  horizontally,  he  determines  the 
position,  on  the  nasal  side,  which  the  movable  mire  must  have 
so  that  he  may  obtain  contact.  He  then  makes  the  same  deter- 
mination, on  the  temporal  side,  after  having  placed  the  arc  ver- 
tically upwards  and  downwards.  These  measurements  give  the 
length  of  the  normals  to  the  cornea  at  four  places,  situated  at 
i  mm.  from  the  visual  line.  He  then  replaces  the  prism  by  an- 
other doubling  2  mm.,  and  so  forth.  Knowing  the  normal  he 
can  then  directly  calculate  the  aberration  produced  by  the  cor- 
responding part  of  the  cornea  (see  chapter  VII). 

We  observe,  furthermore,  that  the  ophthalmometer  lends  itself 
very  well  to  the  examination  of  the  curvature  of  the  surfaces  of 
the  dead  eye.  Holth  thus  made  a  series  of  measurements  in  the 
laboratory  of  the  Sorbonne.  He  placed  the  eye  with  the  cornea 


OPHTHALMOMETRY  73 

upwards  under  a  mirror  at  45°  which  sent  the  reflected  image 
in  the  direction  of  the  ophthalmometer.  The  mirror  must  not 
be  too  small,  for  it  must  allow  us  to  measure  also  the  peripheral 
parts  of  the  surfaces  by  displacing  the  instrument.  As  the 


Fig.  44. — Keratoscopic  images  of  a  cornea  presenting  a  considerable  astig- 
matism at  the  central  -part  (central  ring  of  figure  C).  while  the 
remainder  of  the  cornea  is  nearly  exempt  from  it.  After  Javal. — 
C,  direct  look;  H,  upwards  look;  B,  downwards;  D,  to  the  right; 
G,  to  the  left. 

surfaces  are  generally  more  or  less  misty,  we  are  obliged  to 
coat  them  with  a  very  thin  layer  of  oil  to  make  them  bright.  It 
was  necessary  for  the  measurement  of  the  cornea  to  make  an 
injection  into  the  vitreous  body  so  as  to  make  its  tension  that 
of  the  eye,  but  it  was  interesting  to  note  how  much  he  could 
change  the  tension  of  the  eye  without  observing  any  perceptible 
alteration  in  the  curvature  of  the  cornea.  To  measure  the  curva- 
ture of  the  posterior  surface  of  the  cornea,  Holth  injected  a 
solution  of  gelatine  into  the  anterior  chamber;  as  soon  as  the 
gelatine  solidified  he  removed  the  cornea  and  measured  the 
anterior  surface  of  the  cast,  made  bright  with  oil.  The  anterior 


74 


PHYSIOLOGIC  OPTICS 


surface  of  the  crystalline  lens  is  measured  directly,  after  the 
cornea  and  iris  have  been  removed.  To  measure  the  posterior 
surface  he  cut  the  eye  in  two,  along  the  equator,  and,  the 
vitreous  body  being  removed,  the  eye  was  placed  with  the  cornea 
downwards.  Holth  gave  an  account  of  the  results  achieved  by 
him  at  the  Ophthalmological  Congress  of  Utrecht  in  1899  (see 
also  page  219). 

EXAMINATION  WITH  THE  KERATOSCOPIC  Disc. — The  measure- 
ment df  peripheral  parts  of  the  cornea  takes  too  much  time  to 


Fig.  45. — Keratoscopic  figures  of  a  case  analogous  to  that  of  figure  44. 

After  Javal. 


be  of  service  in  clinics,  but  we  can  obtain  information  about  the 
peripheral  parts  of  the  cornea  by  means  of  the  keratoscopic  disc, 
a  circular  disc,  on  which  are  painted  concentric  circles  of  dif- 
ferent colors.  We  can  place  it  on  the  telescope  of  the  ophthal- 
mometer  by  taking  out  the  double  refracting  prism,  or  simply 
by  holding  it  in  the  hand  and  looking  through  a  central  aperture 
(Placido).  Generally  the  patient  looks  towards  the  middle  of 


OPHTHALMOMETRY  75 

the  disc;  the  images  of  the  circles  are  then  circular  in  a  normal 
eye,  and  elongated  along  the  meridian  of  least  refraction  in  the 
astigmatic  eye;  by  making  the  patient  look  towards  the  border 
of  the  disc  it  is  easy  to  establish  the  peripheral  flattening  of  the 
cornea. 

In  cases  of  irregular  astigmatism  the  circles  assume  irregular 
forms;  and  we  may  often,  by  studying  these  forms,  obtain  im- 
portant information  on  the  anomaly  in  question. — Thus  figs.  44 
and  45  show  the  appearance  of  the  disc  in  cases  in  which  the 
central  part  of  the  cornea  was  affected  with  a  pronounced  astig- 
matism, while  the  middle  zones  were  scarcely  affected  at  all; 
we  see,  in  fact,  that  the  central  ring  of  figure  C,  which  cor- 
responds to  the  middle  of  the  cornea,  is  much  lengthened,  while 
the  more  peripheral  rings  are  almost  circular. — In  cases  of 
keratoconus  the  image  of  the  disc  is  very  small  when  it  is  formed 
at  the  summit  of  the  cornea,  but  the  least  deviation  of  the  look 
causes  a  change  of  form  by  lengthening  it  in  the  radial  direction 


Fig.  46. — Keratoscopic  figures  of  a  case  of  keratoconus.     After  Javal. 


76 


PHYSIOLOGIC  OPTICS 


We  have  seen  (page  44)  that  the  visual  line  passes  through 
the  cornea  perpendicularly  or  nearly  so.  When  making  a  kerato- 
scopic  examination  the  observed  person  looks  into  the  telescope ; 
the  center  of  the  concentric  rings  of  the  image  indicates,  there- 
fore, the  place  where  the  visual  line  passes  through  the  cornea, 
and  if,  at  the  same  time,  we  illuminate  the  eye  moderately  we 
can  account  for  the  direction  of  the  visual  line  relatively  to  the 
different  parts  of  the  eye.  It  may  be  useful  to  modify  the 
appearance  of  the  disc.  Figure  460  shows  the  keratoscopic 

appearance  of  an  eye  af- 
fected with  a  high  de- 
gree of  astigmatism,  and 
of  which  the  angle  a  has 
an  unusual  size;  the 
small  black  circle  indi- 
cates the  pupil,  the 
white  figure  is  the  cor- 
neal  image  of  a  large 
white  disc  provided  with 
a  black  cross,  the  arms 
of  which  were  placed  in 
the  principal  meridians; 
its  elliptical  form  is  due 
to  the  astigmatism.  The 


Fig.    46o. — Keratoscopic    image    of   an   eye 
with    a  large  angle  o. 


Hj  visual   line   corresponds 

to  the  intersection  of  the  two  black  lines.  We  notice  that  it  is 
placed  very  eccentrically  in  the  pupil  so  that  the  four  quadrants  of 
the  latter  are  of  very  different  size.  The  angle  a  was  about  9° ; 


Pig.  466. — Spot  of  Mariotte  of  an  eye  with  a  large  angle  a,  compared  with 
that  (dotted)  of  a  normal  eye.    a,  point  of  fixation. 

the  axis  of  the  crystalline  lens  was  directed  8.8°  outwards  and 
3.8°  downwards  from  the  visual  line. 


OPHTHALMOMETBY 


77 


As  in  every  instance  in  which  the  angle  a  has  an  unusual  size, 
the  cause  was  to  be  found  in  the  displacement  of  the  fovea,  a 
displacement  which,  in  this  case,  manifests  itself  also  by  an 
increased  distance  between  the  point  of  fixation  and  the  blind 
spot  (fig.  46^).  The  internal  border  of  the  latter  was  at  15° 
instead  of  11°  or  12°. 

31.  Measurement  of  the  Angle  a. — For  the  following  measure- 
ments I  use  the  ophthalmophakometer  (fig.  47,  see  page  53).  I 
designate  by  A  the  cursor  which  carries  only  one  lamp;  by  B 


Fig.  47. — The  ophthalmophakometer. 

that  which  carries  two,  placed  on  the  same  vertical  rod,  and 
by  C  the  third  cursor  which  carries  a  rod  on  which  moves  a 
small  bright  ball  which  serves  as  the  point  of  fixation. 

I  place  the  arc  horizontally  and  the  cursor  B  at  the  zero  of 

(1)   The  lamp  of  the  cursor  A  is  not  used  in  this  experiment. 


78  PHYSIOLOGIC  OPTICS 

the  graduation  of  the  arc  (i)  so  that  its  two  lamps  are  in  the 
same  vertical  plane  as  the  middle  of  the  objective  of  the  tele- 
scope, and  I  request  the  observed  person  to  look  towards  this 


Fig.  48. — The  images  of  Purkinje  observed  with  the  ophthalmophakometer. 
The  two  lamps  B,  figure  47,  are  in  the  same  vertical  plane  as  the 
avis  of  the  telescope  and  the  observed  person  looks  at  5.7°  On  the 
nasal  side,  so  as  to  align  the  images.  The  optic  axis  of  the  eye 
coincides  in  these  circumstances  with  the  axis  of  the  telescope. 


Fig.  49. — Position  of  the  images  when  the  observed  person  looks  into  the 
telescope.  The  position  of  the  lamps  is  the  same  as  in  figure  48. 
At  the  middle,  the  corneal  images  on  the  right,  those  of  the  an- 
terior surface  of  the  crystalline  lens;  on  the  left,  those  of  the 
posterior  surface  of  the  crystalline  lens.  The  images  of  the  posterior 
surface  of  the  cornea  are  not  visible. 


OPHTHALMOMETBY 


79 


latter  place.  It  is  clear  that,  if  the  surfaces  of  the  eye  were 
centered  around  the  visual  line,  we  should,  in  these  circum- 
stances, see  the  six  images  of  reflection  on  the  same  vertical  line 
(fig.  48)  (those  of  the  posterior  surface  of  the  cornea  are  not 
visible  under  these  conditions).  But  this  has  never  happened. 
We  always  see,  as  in  fig.  49,  the  images  of  the  anterior  sur- 
face of  the  crystalline  lens,  on  the  one  side,  those  of  the  posterior 
surface  of  the  crystalline  on  the  other,  and  the  corneal  images 
in  the  middle.  I  then  request  the  observed  person  to  fix  the 


Fig.  50. — The  two  lamps  are  in  the  same  horizontal  plane  as  the  axis  of 
the  telescope.     The  observed  person  looks  into  the  telescope. 

bright  ball  of  the  cursor  C,  and  I  displace  this  cursor  until  I 
see  the  images  placed  as  in  fig.  48.  The  optic  axis  of  the  eye  is 
then  in  the  vertical  plane,  passing  through  the  axis  of  the  tele- 
scope, and  the  angular  distance  of  the  cursor  C  from  the  telescope 
indicates  how  much  the  visual  line  deviates  from  the  optic  axis 
in  the  horizontal  plane. — We  find  that  it  is  necessary  to  place 
the  cursor  C  on  the  nasal  side  at  a  distance  from  the  telescope 
varying  between  4°  and  7°  (angle  a). — This  angle  can  be  deter- 
mined with  very  great  exactness. 

I  then  place  the  arc  vertically  so  that  the  two  lamps  are  in  a 
horizontal  plane:  generally  the  six  images  are  not  on  a  horizontal 
line  (fig.  50)  ;  by  displacing  the  cursor  C,  which  the  observed 


80  PHYSIOLOGIC  OPTICS 

person  fixes,  until  I  see  all  the  images  on  a  horizontal  line,  I 
determine  the  vertical  deviation  of  the  visual  line. 

The  optic  axis  is  nearly  always  directed  outwards  from  the 
visual  line,  and  most  frequently  downwards  (2°  to  3°)  ;  some- 
times we  find  it,  however,  in  the  same  horizontal  plane,  or  de- 
viated a  little  upwards. 


Fig.  51. — Defect  of  centering;  it  is  impossible  to  align  the  six  images. 


DEFECT  OF  CENTERING.— We  sometimes  observe  that  it  is  not 
possible  to  place  the  six  images  on  a  straight  line  (fig.  51). 
We  succeed  in  aligning  two  pairs,  whichever  we  want,  but  the 
third  remains  outside.  This  takes  place  when  the  eye  is  not 
exactly  centered ;  that  is  to  say,  when  the  axis  of  the  crystalline 
lens  does  not  pass  through  the  center  of  curvature  of  the  cornea 
(the  posterior  surface  of  which  I  neglect).  We  can  nearly 
always  establish  slight  defects  of  this  kind,  but  most  frequently 
they  are  negligible.  When  we  find  more  considerable  defects, 
it  is  generally  because  the  axis  of  the  crystalline  lens  passes  a 
little  (up  to  0.25  mm.)  above  the  center  of  curvature  of  the 
cornea. 

32.  Determination  of  the  Position  of  the  Internal  Surfaces. — To 
measure  the  radii  of  the  surfaces  we  must  determine:  i°  the 
position  (the  distance  from  the  summit  of  the  cornea)  of  the 


OPHTHALMOMETRY  81 

surfaces;  2°  the  position  of  the  centers.  It  is  true  that  there 
exists,  as  we  shall  see,  a  means  of  determining  the  radii  directly, 
but  we  must  not  forget  that  all  the  sizes  which  we  are  measur- 
ing here  are  apparent  sizes,  and  that,  to  find  the  real  values,  we 
must  reduce  the  results  by  a  calculation  following  the  rules 
which  we  have  already  given  (page  49).  To  make  this  reduc- 
tion it  is  necessary  to  know  the  position  of  the  surfaces,  which 
knowledge  is  likewise  necessary  in  order  that  we  may  be  able 
to  combine  the  surfaces  with  one  another  so  that  we  may  pro- 
ceed to  calculate  the  entire  optic  system. 


Fig.  52. — Method  of  determining  the  position  of  an  internal  surface  of 
the  eye. — Si,  anterior  surface  of  the  cornea;  Ci,  its  center;  Sa,  an- 
terior surface  of  the  crystalline  lens;  Ca,  its  center;  Ci,  Ca,  optic 
axis  of  the  eye. 


I  take  the  anterior  surface  of  the  crystalline  lens,  as  an  ex- 
ample, and  I  suppose  that  we  are  making  the  measurement  in 
the  horizontal  direction.  It  is  useful  to  dilate  the  pupil. 


82  PHYSIOLOGIC  OPTICS 

I  place  the  arc  of  the  instrument  horizontally,  and  I  place  also, 
as  far  away  as  possible  from  the  telescope  the  cursor  A,  the 
lamp  of  which  must  be  sufficiently  brilliant  that  the  image  of 
the  surface  to  be  measured  may  be  quite  visible.  This  done,  1 
place  the  cursor  C,  which  carries  the  mark  of  fixation,  at  a 
place  such  that  the  optic  axis  of  the  eye  may  bisect  the  angular 
distance  between  the  telescope  and  A  ( i ) .  It  is  necessary,  there- 
fore, to  have  previously  measured  the  angle  a.  We  then  displace 
the  cursor  B,  the  lamps  of  which  must  be  very  feeble  so  that 
we  may  see  only  the  corneal  images,  until  the  crystalline  image 
of  A  is  exactly  on  the  same  vertical  as  the  corneal  images  of  B. 
Glancing  at  fig.  52,  it  is  easy  to  see  that  we  now  possess  the 
elements  necessary  to  calculate  the  distance  of  the  anterior  sur- 
face of  the  crystalline  lens  from  the  summit  of  the  cornea,  for 
the  angle  c  is  half  the  angular  distance  of  A  from  the  telescope, 
and  the  angle  d  is  half  of  the  angular  distance  (i)  of  B  from 
the  telescope.  Supposing  that  we  knew  the  radius  of  the  cornea 
Rj,  which  should  have  been  measured  previously,  the  triangle 
O2  C,  P  gives  us  the  relation  O2  Ct  —  R,  8in</  and  we  have 

1       sine  , 

for  the  distance,  looked  for 

Olo2  =  Rx  -  02C,  =  R,  /i  _f!^\=  RJ  sin  c  ~ sin  d 

sin  c 

If  very  great  exactness  is  not  desired,  the  sines  can  be  re- 
placed by  the  arcs. 

EXAMPLE. — Let  the  radius  of  the  cornea  be  7.98  mm.,  the  dis- 
tance of  A  from  the  telescope  28°  nasal,  that  of  B  16.8°  nasal; 
we  will  have  Ol  O2=7.98  (i  — ^™^)=3.i6  mm.  The 
apparent  depth  of  the  anterior  chamber  would,  therefore,  be  3.16 
mm.,  whence  we  find  the  true  value  3.73  mm.  by  placing  in  the 
formula  ^ -f --  =1,  the  values  Fx =23.64,  F2=3i.6i,  /1= 


(1)    We  can   imagine  the  two  lamps   of  B  united   into  one  only,   at  the   level 
of  the  lamp  of  A. 


OPHTHALMOMETRY 


83 


33.  Determination  of  the  Centers  of  the  Internal  Surfaces. — We 
place  A  above  the  telescope,  and  we  move  C  with  the  mark  of 
fixation  as  far  as  possible  from  the  telescope,  but  so  that  the 
image  may  not  disappear  behind  the  iris;  then  we  displace  B 
until  the  corneal  images  of  its  two  lamps  are  on  the  same  ver- 
tical line  as  the  crystalline  image  of  A. 

s'        S* 


Fig.  53. — Method  of  determining  the  position  of  an  internal  surface  of  the 
eye.     The  letters  signify  the  same  as  in  figure  52. 


Under  these  conditions,  the  axis  of  the  telescope  is  perpen- 
dicular to  the  apparent  anterior  surface  of  the  crystalline  lens 


(I)  If   the   eye   is   not   centered   we   must   replace   the   optic    axis   by    the   line 
passing   through    the   center   of   curvature    of   the   cornea   and   the    center   of   the 
surface  which  we  desire  to  measure.     We  find  this  line  as  we  found  the  optic  axis 
in    the   preceding   experiment,    by   aligning   the   corneal    images    witt    the    images 
of  the  surface  to   be  measured. 

(II)  If  we  imagine  the  lamp  placed  at  the  center  of  the  objective,  the  ray  which 
reaches  the  observer's  eye  would  be  reflected  exactly  on   itself,   which  can  take 
place   only   if   it   meets    perpendicularly   the   apparent   surface. 


84  PHYSIOLOGIC  OPTICS 

(II).  We  find  the  angle  a  (fig.  53)  by  adding  (subtracting)  the 
angle  x  to  the  angular  distance  of  C  from  the  telescope.  The 
angle  b  is  half  of  the  distance  of  B  from  the  telescope ;  we  have 
C2C1=^ Rj  sin<*  and  the  distance  sought  equal  to 


Ri/1  +  sin*\  =  R:    /si"  a  +  sin  b\  . 
^         siu  at  I         sin  a         J 


EXAMPLE  —  In  the  same  eye  as  before  let  a=5.i°,  the  distance 
of  B  from  the  telescope  12.4°  temporal  and  that  of  C  from  the 
telescope  9.9°  nasal.  We  would  then  have  for  the  distance 
sought  7.98  (i-f-  sinfi-^°  )  =18.28  mm.  and  the  apparent  radius 


would  be  i8.28mm.  —  3.16  mm.=  i5.i2  mm.    The  position  of  the 
real  center  would  be  13.78  mm.  (i)  and  the  radius  of  the  real 

surface  13.78  mm.  —  3.73=10.05  mm. 

\ 

34.  Direct  Determination  of  the  Kadii.  —  In  fig.  49,  as  well  as 
in  figs.  50  and  51,  the  ratio  between  the  distances  separating 
the  two  images  of  the  same  kind  is  equal  to  the  ratio  between 
the  apparent  radii.  We  may,  indeed,  consider  the  distance 
separating  the  two  lamps  as  an  object,  three  images  of  which 
are  formed  on  the  pupil;  these  images  are  proportional  to  the 
radii  following  the  formula  _2_=J^_,  since  O  and  /  are  the  same 

1  Jv 

in  the  three  cases. 

We  can  make  sufficiently  accurate  measurements  of  the  radii 
if  we  make  use  of  two  cursors  similar  to  A  and  two  others 
similar  to  B.  We  place  the  lamps  A  in  such  a  position  as  to  be 
able  to  observe  clearly  the  images  produced  by  the  anterior 
surface  of  the  crystalline  lens.  Then  we  displace  the  cursors  B, 
the  lamps  of  which  must  be  feeble,  until  the  corneal  images  of 
the  lamps  of  each  are  on  the  same  straight  line  as  one  of  the 
crystalline  images  of  A.  We  consider  the  distance  which 
separates  the  cursors  A  as  object  for  the  anterior  surface  of  the 
crystalline  lens,  and  that  separating  the  cursors  B  as  object  for 


(1)     [Considering    that   we   have    again    obtained    this    apparent    position    with 
reference   to    the    refraction    of   the    cornea,    we    must   therefore    in    the    formula 

*JL  _L  *J?=      1   put  F!   —   23.64  ;   F2  —   31.61   and  ft  — —  18.28,   this   gives   fa 

/i  T  /a 

— 13.78.]— W. 


OPHTHALMOMETRY  85 

the  cornea.  As  the  images  are  alike,  the  radii  must  be  inversely 
proportional  to  the  objects.  Knowing  the  radius  of  the  cornea, 
we  can,  therefore,  calculate  the  apparent  radius  of  the  anterior 
surface  of  the  crystalline. 

To  determine  the  astigmatism  of  the  surface  we  must  re- 
peat all  the  measurements  in  the  vertical  meridian. 

The  posterior  surface  of  the  crystalline  lens  is  measured  ex- 
actly like  the  anterior  surface.  As  to  the  posterior  surface  of 
the  cornea,  its  image  is  not  visible  at  the  middle  of  the  pupil. 
We  must,  therefore,  limit  ourselves  to  measuring  the  peripheral 
parts.  The  direct  determination  of  the  position  of  the  surface, 
following  the  method  indicated  in  paragraph  32,  is  not  applicable 
for  the  same  reason,  but  the  position  of  the  center  can  be  de- 
termined after  paragraph  33,  and  the  length  of  the  radius  as  we 
have  just  explained,  which  gives  indirectly  the  thickness  of  the 
cornea.  It  is  necessary  to  have  previously  measured  the  radius 
of  the  anterior  surface  of  the  cornea  at  the  place  where  we  are 
making  the  measurement,  for  generally  this  place  is  so  peripheral 
that  the  flattening  of  the  cornea  makes  itself  felt.  Besides,  the 
posterior  surface  undergoes,  towards  the  periphery,  a  flattening 
analogous  to  that  of  the  anterior  surface,  so  that  the  relation 
between  the  radii  of  the  two  surfaces  seems  almost  the  same 
everywhere. 


35.  General  Remarks. — We  can,  therefore,  thus  measure  on 
the  living  subject  all  the  optic  constants  except  the  indices.  But 
we  must  not  deceive  ourselves  as  to  the  exactness  ot  these 
measurements;  excepting  those  of  the  anterior  surface  of  the 
cornea;  they  are  not  very  exact.  In  fact,  the  crystalline  images 
are  feeble,  and  those  of  the  anterior  surface  of  the  crystalline 
lens  very  diffuse,  which  causes  the  measurement  to  become  less 
certain;  there  are  also  other  sources  of  errors,  such  as  that 
made  by  comparing  the  surfaces  to  spherical  surfaces,  it  may 
happen  also  that  the  observed  eye  does  not  fix  exactly  at  the 
moment  of  observation.  When  we  wish  to  determine,  for  ex- 


86  PHYSIOLOGIC  OPTICS 

ample,  the  radius  of  the  anterior  surface  of  the  crystalline  lens, 
we  have  to  depend  on  three  measurements,  that  of  the  radius 
of  the  anterior  surface  of  the  cornea,  that  of  the  position  of  ttie 
anterior  surface  of  the  crystalline,  and  that  of  the  position  of 
its  center.  The  errors  of  these  measurements  are  added  in  the 
final  result.  I  do  not  think,  therefore,  that  we  can  guarantee 
an  exactness  of  more  than  half  a  millimeter  in  the  final  result. 
As  far  as  the  optics  of  the  eye  are  concerned,  this  want  of  ex- 
actness does  not  present  any  considerable  importance.  Indeed, 
it  must  not  be  forgotten  that  the  difference  of  index  of  the  media 
which  separate  the  internal  surfaces  is  very  slight,  making  it  un- 
necessary to  know  the  radii  very  exactly;  an  error  of  half  a 
millimeter  in  the  measurement  of  the  anterior  surface  of  the 
cornea  corresponds  to  about  3  D.,  whilst  the  same  error  in  the 
measurement  of  the  anterior  surface  of  the  crystalline  lens  cor- 
responds only  to  a  third  of  a  dioptry. — But,  as  to  the  thickness 
of  the  crystalline  lens,  which  is  only  4  mm.,  an  error  of  half  a 
millimeter  presents  a  vast  importance.  The  much  disputed 
question  of  knowing  whether  the  crystalline  lens  changes  its 
thickness  during  accommodation  can  with  difficulty  be  decided 
by  the  observation  of  the  crystalline  images,  for  the  alleged 
change  (an  increase  of  0.4  mm.)  does  not  exceed  the  limit  of 
error. 

Ophthalmometry  of  the  cornea  has  passed  the  doors  of  the 
laboratories,  and  has  been  introduced  into  clinics  where  it  is 
daily  rendering  great  service.  It  might  be  asked,  therefore, 
whether  the  measurements  of  the  internal  surfaces  could  not 
also  find  clinical  application.  Indeed  there  often  exist  between 
the  astigmatism  indicated  by  the  ophthalmometer  and  subjective 
astigmatism,  differences  the  cause  of  which  it  is  very  natural 
to  look  for  in  the  internal  surfaces,  and  which  we  might  hope 
to  disclose  by  these  methods.  I  have  made  some  measurements 
of  this  character,  but  I  do  not  think  they  have  a  great  future. 
They  are  always  very  complicated;  it  would  be  necessary,  in 
fact,  to  measure  the  radius  of  each  surface  at  least  in  two 
meridians,  and  as  each  radius  calls  for  two  measurements  (of  the 
surface  and  the  center)  this  would  involve  already  12  measure- 


OPHTHALMOMETEY  87 

ments;  it  would  then  be  necessary  for  us  to  calculate  the  real 
values  in  order  to  deduct  the  astigmatism  of  each  surface  and 
lastly  to  combine  these  astigmatisms  with  that  of  the  anterior 
surface  of  the  cornea.  This  is  already  sufficiently  complicated, 
but  it  becomes  more  so  if,  as  is  probable,  the  main  meridians 
of  ihe  internal  surfaces  coincide  neither  with  one  another  nor 
with  those  of  the  anterior  surface  of  the  cornea. — It  is  true 
that  5t  would  be  possible  to  simplify  the  methods  for  practical 
application,  and  to  replace  the  calculations  by  approximations, 
but  I  do  not  think  the  result  is  worth  the  trouble,  more  especially 
as  it  is  probable  that  we  frequently  would  not  find  what  we  look 
for,  the  explanation  of  the  differences  between  ophthalmometry 
and  subjective  astigmatism,  for  these  differences  are  probably 
frequently  due  to  the  fact  that  the  peripheral  parts  of  the  cornea 
have  an  astigmatism  different  from  that  of  the  central  parts, 
which  we  measure  with  the  ophthalmometer. 

Bibliography. — Aubert  (H.).  Pfluger's  Archiv.  Bd.  35,  p.  597,  1885. 
— Javal  (E.).  Memoires  d'ophthalmometrie.  Paris,  1890. — Sulzer  (D.). 
La  forme  de  la  cornee  hurrMine  et  son  influence  sur  la  vision.  Arch,  d'opht., 
1891. — Eriksen.  Hornliindemaalinger  (Danish).  Arahus,  1893. — Tschern- 
ing  (M.).  Beitrage  zur  Dioptrik  des  Auges  (Zeitschrift  fur  Psychologic 
und  Physiologic  der  Sinnesorgane,  III,  p.  429). — Brudzewski  (K.).  Beitrag 
zur  Dioptrik  des  Auges.  Arch,  fur  AugenheilTcunde.  XL,  3. 


CHAPTER  V 
CIRCLES  OF  DIFFUSION  ON  THE  RETINA 

36.  Definition. — Receiving  on  a  screen  the  image  of  a  distant 
luminous  point,  and  moving  the  screen  forwards  and  backwards, 
we  see  that  there  is  only  one  position  in  which  there  is  formed 
a  distinct  image  of  the  point.  In  every  other  position  we  see  on 
the  screen  a  luminous  spot  of  the  same  form  as  the  aperture 
of  the  lens,  which  spot  is  the  larger  the  farther  it  is  removed 
from  the  distinct  image.  This  luminous  spot  is  called  circle  oj 
diffusion. 

The  same  thing  happens  in  the  eye,  with  this  difference  that, 
not  being  able  to  move  the  retina  backwards  or  forwards,  we 
move  the  luminous  point  which  amounts  to  the  same.  The 
round  form  of  the  image  of  diffusion  is  due  to  the  round  form 
of  the  pupil ;  if  we  look,  for  example,  through  an  aperture  which 
is  triangular  and  smaller  than  the  pupil,  the  image  of  diffusion 

is  triangular  and  is  some- 
w  h  a  t  improperly  called 
circle  of  diffusion. 

It  is  easy  to  calculate 
the  size  of  the  circle  of 
diffusion  (fig.  54).    If  the 
Fig.  54.  diameter  of  the  pupil  (of 

exit)  be  designated  by  p, 

its  distance  from  the  retina  by  a  and  the  distance  of  the  distinct 
image  from  the  retina  by  d,  we  have  for  the  diameter  of  the 
circle  of  diffusion  the  expression 

*=>7T-.' 

If,  instead  of  a  luminous  point,  we  observe  an  object  the 
image  of  which  is  formed  in  front  of  or  behind  the  retina,  each 
point  of  the  object  produces  on  this  membrane  a  circle  of  diffus- 
ion which  is  overlapped  by  the  next  circle,  except  near  the 

88 


CIRCLES  OF  DIFFUSION  ON  THE  RETINA  89 

borders  of  the  diffuse  image.  There  is  also  formed  around  the 
shape  of  the  object  a  border,  the  width  of  which  is  equal  to 
half  of  the  diameter  of  a  circle  of  diffusion,  and  the  intensity 
of  which  diminishes  towards  the  periphery.  The  object  is, 
therefore,  seen  a  little  enlarged  and  with  ill-defined  borders. 

I 

37.  Line  of  Sight. — When  we  perform  the  act  of  sighting  we 

try  to  make  two  points,  situated  at  different  distances,  coincide; 
as  we  can  only  see  one  point  distinctly  at  once,  it  is  generally 
supposed  that  we  make  the  image  of  one  of  the  points  coincide 
with  the  center  of  the  circle  of  diffusion  of  the  other.  Now  the 
center  of  the  circle  of  diffusion  corresponds  with  the  middle  of 
the  pupil;  it  would  be  necessary,  therefore,  to  place  the  second 
point  on  the  line  which  joins  the  point  which  is  fixed  to  the 
center  of  the  apparent  pupil,  a  line  which  is  called  the  line  of 
sight.  This  reasoning  is  subject  to  caution.  Indeed,  in  order 
to  be  able  to  sight,  it  is  necessary  to  see  the  second  point  pretty 
distinctly,  which  requires  that  it  be  not  too  far  removed,  optically, 
from  the  point  fixed.  The  circle  of  diffusion  of  the  point  ot 
sight  is,  therefore,  so  small  that  we  commit  only  a  very  small 
error  when  we  consider  it  as  a  point.  We  must  also  note  that 
the  rule  according  to  which  the  circle  of  diffusion  should  every- 
where have  the  form  of  the  pupil,  is  not  strictly  correct.  By 
reason  of  astigmatism  and  other  irregularities  of  the  eye,  there 
nearly  always  exists,  as  we  shall  see  in  chapter  X,  a  part  in 
front  of  or  behind  the  focus,  where  the  circle  of  diffusion  is  far 
from  having  the  form  of  the  pupil;  it  assumes  more  or  less  ir- 
regular forms,  and  the  light  is  no  longer  distributed  in  a  regular 
manner.  In  sighting,  then,  we  make  the  image  of  the  point  fixed 
coincide  with  the  brightest  part  of  the  circle  of  diffusion,  which 
has  nothing  to  do  with  the  center  of  the  pupil.  In  order  not  to 
complicate  the  terminology,  it  would,  therefore,  be  preferable  to 
dispense  with  the  expression  line  of  sight. 

38.  Accommodation. — We  know  that  the  eye  can  change  its 
focus,  adapting  itself  for  shorter  distances  than  that  for  which 
it  is  adapted  in  a  state  of  repose.    Holding  a  book  at  50  centi- 


90 


PHYSIOLOGIC  OPTICS 


meters  and  placing  a  veil  between  the  book  and  the  eyes,  at  20 
centimeters,  we  can  see  distinctly,  sometimes  the  threads  of  the 
veil,  and  sometimes  the  letters. — If  we  illuminate  the  fundus 
of  an  emmetropic  eye  with  the  aid  of  a  plane  mirror,  by  using 
a  flame  placed  at  a  great  distance,  we  see  a  distinct  image  of 
the  flame  projected  on  the  fundus  of  the  eye,  if  the  observed 
person  looks  in  the  distance.  If,  on  the  contrary,  he  fixes  an 
object  located  nearer,  the  image  forms  a  circle  of  diffusion 
which,  most  frequently,  fills  the  entire  pupil.  The  contrary 
takes  place  when  the  flame  is  placed  at  a  short  distance. 


t> 

Fig.  55.-— Eules  of  the  optometer  of  Young. 

39.  Experiments  of  Czermak,  Scheiner  and  Mile. — Looking 
towards  an  illuminated  surface  (the  sky,  for  example)  through 
a  pin-hole  made  in  a  dark  screen,  we  see  the  opening  under  the 
form  of  a  circle  of  diffusion.  If  we  move  a  second  screen,  held 
nearer  the  eye,  in  front  of  the  opening,  it  seems  to  move  in  a 
direction  contrary  to  that  in  which  it  really  does  move.  If,  on 
the  other  hand,  we  move  the  second  screen  in  front  of  the  first, 
it  seems  to  move  in  the  direction  of  its  real  displacement  (Czer- 
mak). 

Looking  towards  an  illuminated  surface  through  two  openings, 


CIRCLES  OF  DIFFUSION  ON  THE  RETINA  91 

the  distance  of  which  is  smaller  than  the  diameter  of  the  pupil, 
we  see  two  circles  of  diffusion  which  partly  overlap.  A  needle 
is  then  placed  so  that  we  see  it  in  the  part  common  to  the  circles 
of  diffusion,  and  another  farther  away  in  the  same  direction. 
That  one  of  the  two  needles  which  we  fix  is  seen  single,  the 
other  double.  If  it  is  the  nearer  needle  that  is  seen  double,  the 
image  on  the  left  disappears,  if  we  cover  the  opening  on  the 
right,  (i)  If  it  is  the  other  needle  that  is  seen  double,  the 
contrary  takes  place  (Scheiner). — It  is  easy  to  repeat  this  ex- 
periment with  a  lens,  and  it  is  also  a  very  good  way  of  deter- 
mining the  focal  distance  of  the  latter  (by  replacing  the  needle 
by  a  luminous  point). 

If  we  look  at  the  more  distant  of  the  two  needles  in  the 
experiment  of  Scheiner  through  a  single  small  opening,  we  shall 
see  that  a  slight  movement  of  the  screen  causes  the  nearest 
needle  to  move  in  the  contrary  direction.  On  fixing  the  nearer 
of  the  two  needles  the  other  seems  to  move  in  the  same  direction 
as  the  screen  (Mile). 

It  is  easy  to  account  for  these  phenomena  when  we  sketch  the 
course  of  the  rays,  not  forgetting  that  the  eye  inverts  the 
phenomena  when  projecting  them  outwards. 

40.  Optometer  of  Thomas  Young.  (2) — The  experiment  of 
Scheiner  forms  the  basis  of  the  optometer  of  Thomas  Young, 


(1)  To  render  the  experiment  more  striking  to  my  pupils,  I  had  a  plate  of  red 
gelatine  glued  in  front  of  the  opening  on  the  right.     But,  after  having  explained 
the  theory   of   the  experiment,   I   met  with   very  vigorous   protestations ;    all   de- 
clared that  it  was  the  needle  on  the  right  which  appeared  red.     It  is  thus,  in  fact, 
when  we  look  towards  the  sky,  but  we  must  not  conclude  from  this  that  it  is  the 
needle  on  the  right  which  belongs  to  the  opening  on  the  right.     The  phenomenon 
is  analogous  to  that  of  colored  shadows,  of  which  I  will  speak  in  chapter  XJVII. 
If  one   places  oneself   in   such    a  way   that   the   needle   is    eliminated,    it   is    the 
image  on  the  left  which  appears  red.     One  of  my  pupils,  M.  Johnsson,  has  studied 
the   chromatic   phenomena  which   are   observable  under   the   same  circumstances, 
by  looking  at  the  needle  towards   the  sky,   but  without  the   interposition   of   the 
colored  plate.     One  sees  them  specially  well  by  dilating  the  pupil  and  using  the 
slits  of  the  optometer  of  Young.     When  the  needle  is  situated  on  the  near  side 
of  the  point  which  is  fixed,   one  of  the  images  is  seen  green,   the  other  purple ; 
each  image  is  bordered  with  red  on  the  side  which  looks  towards  the  other  image, 
with  blue  on  the  opposite  side.     These  phenomena,  which  depend  on  the  chromatic 
aberration  of  the  eye,  are  not  yet  well  explained. 

(2)  Not  being  able  to  procure  any  part  of  this  instrument,  I  had  it  constructed 
again  by  M.  Werlein,  modernizing  it  a  little. 


92  PHYSIOLOGIC  OPTICS 

which  appears  to  me  to  be  one  of  the  most  important  instruments 
for  the  study  of  physiologic  optics.  It  has  the  form  of  a  little 
rule.  On  one  of  the  faces  is  drawn  a  fine  white  line  on  a  black 
ground.  We  look  along  this  line,  through  a  lens  of  +  10  D.  In 
front  of  the  lens  moves  a  small  horizontal  rule,  in  which  are 
different  groups  of  slits  (fig.  550).  Placing  the  two  slits,  which 
are  at  the  middle  of  the  horizontal  rule,  in  front  of  the  lens, 
they  act  like  the  openings  in  the  experiments  of  Scheiner.  Each 
point  of  the  line  appears  double,  except  that  which  is  seen  dis- 
tinctly; an  emmetrope,  not  using  his  accommodation,  must, 
therefore,  see  two  lines  which  intersect  at  the  punctum  remotum, 
or  artificial  far  point,  at  10  cm.  from  the  eye.  To  determine  the 
refraction  of  any  person  we  make  him  look  in  the  instrument, 
and  put  a  small  cursor  at  the  place  where  he  sees  the  lines  Inter- 
sect. A  dioptric  scale,  placed  along  the  line,  then  permits  the 
refraction  to  be  read  off  directly. — We  then  determine  the  near 
point  (punctum  proximum)  in  the  same  manner. — The  other 
groups  of  slits  permit  the  determination  of  the  refraction  of  the 
different  parts  of  the  pupillary  space.  We  can  also  use  the  little 
vertical  rule  (fig.  51^)  which  has  the  form  of  a  very  pointed 
triangle;  by  lowering  it  more  or  less,  we  eliminate  a  smaller  or 
greater  part  of  the  middle  of  the  pupil. 

The  instrument  does  not  lend  itself  very  well  to  the  examina- 
tion of  patients,  for  it  is  quite  difficult  for  an  inexperienced 
observer  to  use  it  without  using  his  accommodation.  For  one 
who  can  control  his  accommodation,  the  instrument  permits  the 
measurement  simultaneously  of  the  refraction  and  the  amplitude 
of  the  accommodation;  the  refraction  can  be  determined  in 
different  meridians  by  making  the  instrument  rotate  around  its 
longitudinal  axis.  It  was  thus  that  Young  discovered  the  astig- 
matism of  his  own  eye. 

The  observations  made  with  this  optometer  are,  moreover,  of 
the  greatest  importance  for  the  study  of  the  nature  of  accommo- 
dation (see  chapter  XII). 

41.  Effects  of  the  Stenopaic  Opening. — Looking  through  an 
opening  smaller  than  the  pupil,  we  diminish  the  circles  of  dif- 


CIECLES  OF  DIFFUSION  ON  THE  EEIINA 


93 


fusion  so  that  objects  which  we  first  see  dimly  become  more 
distinct.  This  is  why  myopes  see  better  at  a  distance  by  looking 
through  a  small  opening.  We  can  also  make  use  of  it  as  a 
magnifying  glass;  we  can,  indeed,  move  very  close  to  the  eye 
the  object  which  we  desire  to  examine,  and  in  this  way  obtain 
a  very  large  retinal  image.  The  more  the  diameter  of  the  open- 
ing is  diminished,  the  more  distinct  the  image  becomes,  but  it 
loses  at  the  same  time  in  brightness.  We  cannot  exceed  a 
certain  minimum  limit  without  blurring  by  diffraction  the  dis- 
tinctness of  the  image,  (i) 

As  the  stenopaic  opening  effaces,  so  to  speak,  the  effect  of 
the  anomalies  of  refraction,  it  is  harmful  in  all  cases  in  which 
we  desire  to  determine  refraction.  This  is  why  we  place  patients 
with  their  backs  towards  the  window  when  we  examine  their 
vision.  We  must  also  avoid  the  small  apertures  in  the  ophthal- 
moscopes which  are  used  to  determine  refraction;  a  too  strong 
illumination  is  equally  hurtful. 


Fig.  56. — Magnification  by  means  of  the  stenopaic  opening. 

Examining  an  object  placed  very  near  the  eye  through  a 
stenopaic  opening,  we  shall  see  that  the  object  seems  to  enlarge 
as  we  gradually  move  the  screen  away  from  the  eye.  Following 
is  the  explanation  of  this  fact. 

Let  AB  (fig.  56)  be  an  object,  and  A1B1  its  image  formed  by 
the  optic  system  of  the  eye.  As  the  object  is  near  the  eye,  the 


(1)  Looking  at  a  luminous  point  which  we  see  distinctly,  through  a  very  fine 
opening,  we  observe  that  it  becomes  enlarged  into  a  small  luminous  surface 
surrounded  with  brilliant  rings.  This  effect  of  diffraction  begins  to  make  itself 
slightly  felt  starting  from  an  aperture  of  the  pupil  or  of  the  opening  of  about 
2  millimeters. 


94  PHYSIOLOGIC  OPTICS 

image  is  formed  quite  a  distance  behind  the  retina.  To  deter- 
mine the  position  of  the  indistinct  image  on  the  retina,  we  draw 
the  ray  Ac  passing  through  the  middle  of  the  pupil  of  entrance ; 
after  refraction  it  continues  its  course  as  if  it  came  from  clt  the 
center  of  the  pupil  of  exit.  Its  direction  is  A'c1?  since  it  must 
pass  through  A',  the  image  of  A.  The  point  a  is,  therefore,  the 
middle  of  the  circle  of  diffusion  which  A  forms  on  the  retina, 
and  ab  is  the  diameter  of  the  image  of  diffusion. — Let  us  now 
interpose  the  screen  EE  with  its  stenopaic  opening.  The  only 
ray  which  passes  from  A  through  this  opening  takes  the  direc- 
tion AK  and,  after  refraction,  the  direction  K^A';  it  meets  the 
retina  at  a1  and  a^  b1  is  the  size  of  the  retinal  image.  We  see 
that  this  image  is  larger  than  ab  and  that  it  would  become  larger 
still  if  we  moved  the  screen  farther  away. — Myopes  looking  at 
distant  objects  through  a  stenopaic  opening  see  them  diminish 
if  the  opening  be  moved  away  a  little. 

Bibliography. — The  study  of  the  influence  of  circles  of  diffusion  on 
vision  has  been  very  much  neglected  by  modern  authors.  The  best  work 
done  on  this  question  is  the  following,  which  dates  from  the  last  century: 

Jurin  (J.).  Essai  sur  la  vision  disti/ncte  et  indistincte,  in  Robert  Smith, 
Cours  complet  d'optique,  translated  by  Pezenas,  Paris,  1767. — Scheiner 
(C.).  Oculus.  Innspruck,  1619. — Mile  (J.).  Fogg.  Ann.,  XLII,  40. — 
csuvres  de  Young,  edited  by  Tscherning,  page  112. — Tscherning  (M.). 
L'optometre  de  Young  et  son  empldi'.  Arch,  de  physiol.  October,  1894. 


CHAPTER  VI 
ANOMALIES  OF  REFRACTION 

42.  General  Remarks. — We  have  thus  far  treated  the  optic 
system  of  the  eye  as  if  it  were  perfect,  but  it  has  really  many 
defects.  Helmholtz  said  that  if  an  optician  had  delivered  to  him 
an  optic  instrument  as  imperfectly  made  as  the  eye,  he  would 
have  considered  himself  within  his  right  in  refusing  it ;  express- 
ing himself  in  quite  forceful  language.  The  remark  of  M. 
Mascart  appears  to  me  nearer  the  truth.  He  said  that  the  eye 
has  all  possible  defects,  but  only  to  such  an  extent  that  they 
are  not  harmful.  We  have  already  seen  that  this  is  the  case 
with  diffraction,  which  begins  to  make  itself  felt,  starting  from 
a  pupillary  diameter  of  2  millimeters,  almost  the  lowest  limit 
of  this  diameter.  It  is  the  same  with  chromatic  aberration, 
spherical  aberration,  etc.  An  optician  need  not  be  so  careful 
with  an  objective,  the  images  of  which  are  intended  to  be  magni- 
fied five  times,  as  with  another  the  images  of  which  are  to  be 
magnified  twenty  or  thirty  times.  In  the  same  way  eyes  fre- 
quently have  all  the  visual  activity  we  can  expect  considering 
the  retinal  structure,  and  a  greater  degree  of  optic  perfection 
would  be  superfluous.  It  is  true  that  many  eyes  which  are 
considered  normal,  have  optic  defects  which  diminish  their  visual 
acuity,  which  should  be  nearly  double  that  called  normal  acuity; 
but  for  most  occupations,  the  acuity  known  as  normal  amply 
suffices. 

WTe  can  divide  anomalies  of  refraction  into  three  groups : 

i°.  ANOMALIES  "OF  THE  SCREEN." 

a.  Axial  myopia. — Screen  is  too  far  away   from  the   optfc 
system. 

b.  Axial  hypermetropia. — Screen  is  too  near  the  optic  system, 
r.  Oblique  position  of  the  screen. — This  last  anomaly  is  not 

generally  recognized.    It  seems  to  play  a  part  in  diminishing  the 
visual  acuity  in  certain  forms  of  very  high  myopia,  in  which  the 

95 


96  PHYSIOLOGIC  OPTICS 

summit  of  the  staphyloma  does  not  correspond  exactly  wrth  the 
•fovea.  It  is  evident  that,  if  the  optic  system  of  the  eye  were 
perfect,  all  the  rays  emanating  from  a  point  would  meet  exactly 
in  a  point  on  the  screen,  and  the  obliquity  of  the  latter  would 
play  no  part,  for  the  extent  of  distinct  vision  is  so  small  that 
the  difference  of  distance  of  the  different  parts  of  the  image 
from  the  optic  system  cannot  have  much  influence.  But  if  the 
rays  do  not  meet  exactly  in  a  point,  as  is  nearly  always  the  case, 
it  is  clear  that  the  circle  of  diffusion  on  the  retina  must  be  larger 
when  the  retina  is  placed  obliquely,  and  that  this  must  diminish 
visual  acuity. 

2°.  ANOMALIES  OF  THE  REFRACTING  SURFACES. 


Myopia  )      . 

(  of  curvature. 


Hypermetropia 

Regular  astigmatism. 

Spherical  aberration. 

Chromatic  aberration. 

Keratoconus. 

Lenticonus. 

Aphakia. 

Luxation  of  the  crystalline  lens. 

All  the  forms  which  are  classified  under  the  name  of  irregular 
astigmatism. 

• 

3°.  ANOMALIES  OF  THE  INDICES. 

False  lenticonus. 

The  anomally  which  Demicheri  has  recently  described  under 
the  name  of  false  lenticonus  is  the  only  anomaly  of  the  indices 
which  has  been  established  up  to  the  present.  In  these  cases 
we  see  with  the  ophthalmoscope  the  same  play  of  shadows  that 
is  characteristic  in  keratoconus ;  it  is  due  to  a  great  difference  of 
refraction  between  the  middle  of  the  pupil  which  is  very  myopic 
(as  high  as  10  D.  and  more),  and  the  periphery  which  is  hyper- 
metropic  (3  to  4  D)  The  explanation  is  probably  to  he  found 
in  a  diminution  of  the  index  of  the  peripheral  layers  of  the  crys- 
talline lens,  a  change  which  must  diminish  the  refraction  of  the 


ANOMALIES  OF  EEFEACT10N  97 

peripheral  parts  of  the  pupil  and  greatly  increase  the  central 
refraction,  following  the  explanation  which  we  have  given  on 
page  36.  We  find  in  these  cases  the  images  of  Purkinje  doubled 
(see  page  35),  the  surfaces  of  the  nucleus  giving  rise  to  a  quite 
regular  reflection;  these  cases  are  analogous  to  that  which  I 
have  found  in  the  case  of  the  eye  of  a  dead  ox,  probably  also 
due  to  the  imbition  of  water  by  the  superficial  pans. 

43.  General  Remarks  on  Ametropia. — We  designate  as  the  far 
point  (punctum  remotwm)  the  place  for  which  the  eye  is  focused 
when  in  a  state  of  repose.  It  is,  therefore,  the  conjugate  focus 
of  the  fovea.  By  making  an  effort  of  accommodation,  the  eye 
can  focus  itself  for  shorter  distances.  The  nearest  point  for 
which  the  eye  can  adapt  itself  is  called  the  near  point  (punctum 
proximum).  We  generally  express  the  distance  of  the  near 
point  and  that  of  the  far  point  in  dioptrics;  the  difference  be- 
tween the  two  numbers  is  called  the  amplitude  of  the  accom- 
modation. The  determination  of  the  far  point  is  quite  easy,  ana 
forms  an  important  part  of  the  work  of  the  oculist ;  that  of  the 
near  point  is  not  very  certain,  since  its  position  depends  on  an 
effort  of  the  patient,  the  strength  of  which  may  vary  from  day 
to  day;  for  that  reason  the  determination  of  the  near  point  is 

frequently  neglected  in  clinics. 
• 

We  consider  as  normal  the  emmetropic  eye,  that  is  to  say,  an 
eye  such  that,  in  a  state  of  repose,  the  image  of  distant  objects 
is  formed  on  the  retina.  In  the  myopic  eye  this  image  is  formed 
in  front  of,  in  the  hypermetropic  eye  behind,  the  retina.  We 
designate  these  two  anomalies  under  the  common  name  ot 
ametropia.  The  emmetropic  eye  has  its  far  point  situated  at 
infinity,  that  of  the  myopic  eye  is  at  a  finite  distance1.  A's  to 
the  hypermetropic  eye,  its  remote  point  is  virtual.  It  is  neces- 
sary that  the  rays  converge  before  entering  the  eye  in  order 
that  they  may  reunite  in  a  point  on  the  retina.  This  point  to- 
wards which  the  rays  must  converge,  before  entering  the  eye, 
and  which  is  consequently  situated  behind  the  latter,  is  the  far 
point;  its  distance  is  to  be  put  down  as  negative.  The  degree  of 


98  PHYSIOLOGIC  OPTICS 

ametropia  is  indicated  by  expressing  in  dioptrics  the  distance  of 
the  eye  from  the  remote  point,  (i) 

In  the  great  majority  of  cases,  myopia  and  hypermetropia  are 
due  to  an  anomally  in  the  length  of  the  eye:  the  myopic  eye  is 
too  long,  the  hypermetropic  eye  too  short.  An  increase  or  a 
diminution  of  I  millimeter  in  the  axis  of  the  eye  corresponds 
to  an  ametropia  of  two  dioptrics  and  a  half.  Let  us  place  in  the 
formula  of  Newton,  Z^— F 'jFg,  the  values  of  the  simplified  eye 
F1=i7  millimeters,  F2=22.7,  and  we  will  have  /^g— 386,  in 
which  formula  /x  is  the  distance  of  the  far  point  from  the  an- 
terior focus  and  12  the  distance  of  the  retina  from  the  posterior 
focus  of  the  eye.  If  12=  i  millimeter,  ^—386  millimeters,  which 
corresponds  to  about  2.5  D. ;  if  /2=2  millimeters,  ^=193  milli- 
meters or  about  5  D.,  and  so  on. 

Myopia  is  corrected  by  placing  in  front  of  the  eye  a  concave 
glass  so  that  the  image  which  it  forms  of  distant  objects  may  be 
situated  at  the  far  point  of  the  eye.  On  account  of  the  distance 
of  the  glass  from  the  eye  its  focal  distance  is  a  little  shorter  than 
the  distance  of  the  eye  from  its  far  point.  The  subjective  ex- 
amination always  results,  therefore,  in  our  finding  a  somewhat 
higher  myopia  than  really  exists.  The  difference  is  insignificant 
for  low  degrees  of  myopia,  considerable  for  high  degrees.  If 
we  move  the  glass  away  from  the  eye,  its  effect  diminishes. — 
When  selecting  the  correcting  glass,  we  must  take  great  care  to 
select  the  weakest  concave  glass  which  corrects,  because  young 
myopes  see  as  well  with  stronger  glasses,  the  excess  of  correc- 
tion being  neutralized  by  accommodation.  After  having  found 
the  correcting  glass,  we  may  try  the  effect  of  moving  it  gradually 
away  from  the  eye.  If  the  patient  continues  to  see  well  the  glass 
is  too  strong. 

Hypermetropia  is  corrected  by  means  of  a  convex  glass,  which 
brings  the  image  of  the  distant  object  to  the  far  point  situated 


(1)  From  which  part  of  the  eye  one  should  start  to  calculate  ametropia  is  a 
disputed  question ;  it  seems  to  me  that  the  simplest  way  is  to  calculate  it, 
starting  from  the  summit  of  the  cornea.  Some  have  preferred  to  calculate  it 
from  one  or  other  of  the  cardinal  points  of  the  optic  system,  but  as  these  points 
have  not  the  same  position  in  all  eyes,  nor  in  all  the  meridians  of  the  same  eye, 
nor  even  for  all  parts  of  the  same  meridian,  confusion  would  result. 


ANOMALIES  OF  REFRACTION 


99 


behind  the  eye.  The  focal  distance  of  the  glass  being  a  little 
greater  than  the  distance  of  the  eye  from,  the  far  point,  the  cor- 
recting glass  is  a  little  weaker  than  the  hypermetropia.  The 
hypermetrope  can  increase  the  strength  of  his  glasses  by  moving 
them  a  little  away  from  the  eye. — The  correcting  glass  is  the 
strongest  convex  glass  which  the  patient  tolerates  without  loss 
of  visual  acuity,  but  he  can  also  see  as  well  with  weaker  glasses 
by  using  his  accommodation. 


Fig.  57. 

The  retinal  image  of  an  object  seen  under  a  given  angle  is 
larger  in  the  myopic  eye  and  smaller  in  the  hypermetropic  eye 
than  in  an  emmetropic  eye,  because  the  distance  of  the  posterior 
nodal  point  from  the  retina  is  greater  in  the  myopic  eye,  less  in 
the  hypermetropic  eye. — But,  this  effect  disappears  when  we 
correct  the  ametropic  eye,  by  placing  the  correcting  glass  so  that 
its  optic  center  coincides  with  the  anterior  focus  of  the  eye. 
Then  the  image  is  always  the  same  size,  whatever  the  ametropia 
may  be.  For,  the  rays  AO  and  BO  (fig.  57)  pass  through  the 
lens  without  deviation  and  are  parallel,  after  refraction  by  the 
same  optic  system  of  the  eye,  so  that  the  size  of  the  image  is 
always  the  same,  whatever  may  be  the  distance  of  the  retina. — 
If  we  place  the  correcting  glass  in  front  of  the  anterior  locus, 
the  retinal  image  of  the  myopic  eye  is  smaller,  that  of  the  hyper- 
metropic eye  larger,  than  the  image  of  the  emmetropic  eye, 
which  is  easy  to  see  by  a  construction  analogous  to  that  of  fig. 
57.  We  first  construct  the  image  formed  by  the  glass,  and  draw 
the  rays  passing  through  the  extremities  of  this  image  and 
through  the  anterior  focus. 


100  PHYSIOLOGIC  OPTICS 

Patients  often  say  that  the  concave  glasses  diminish  objects. 
This  may  be  attributed  to  the  fact  that  the  glass  is  placed  in 
front  of  the  anterior  focus,  or  simply  to  the  fact  that  exterior 
objects,  seen  distinctly,  appear  smaller,  because  of  the  disap- 
pearance of  the  circles  of  diffusion.  But  the  cause  may  also  be 
that  the  glass  is  too  strong ;  for  if  the  patient  uses  his  accommo- 
dation the  anterior  focus  approaches  the  eye  and  the  image 
becomes  smaller  for  this  reason. 

44.  Optometers.— The  use  of  the  test  case  lenses  and  of  the 
visual  acuity  chart,  placed  at  a  distance,  is  always  the  best  of  the 
subjective  methods.  A  very  great  number  of  optometers  have 
been  constructed,  but  none  of  them  has  succeeded  in  superseding 
the  test  case;  they  have  this  defect  in  common  that  they  super- 
induce an  effort  of  accommodation  which  makes  the  myopia 
appear  too  strong.  The  best  are  those  which  are  operated  at  a 
great  distance,  like  the  optometer  of  Javal,  but  even  these  seem 
sometimes  to  give  too  strong  degrees  of  myopia.  The  optometer 
of  Javal  is  composed  of  two  discs,  nearly  like  the  discs  of  the 
ophthalmoscope  for  refraction,  but  much  larger :  one  of  the  discs 
has  spherical  lenses,  the  other  cylindrical  lenses;  a  special  me- 
chanism permits  the  axis  of  all  the  cylindrical  lenses  to  be  ad- 
justed in  the  direction  we  desire. — Other  optometers  are  founded 
on  the  use  of  a  single  convex  lens;  by  displacing  the  object  in 
relation  to  this  lens,  we  can  form  the  image  of  it  at  any  distance 
whatever,  and  thus  find  the  place  where  it  appears  distinct.  Op- 
tometers of  this  kind  have  been  constructed  by  Coccius,  Bonders, 
Sous,  and  many  others.  The  optometer  of  Graefe  was  a  Galilean 
telescope;  we  know  that  myopes  are  obliged  to  shorten  their 
opera  glasses  to  see  distinctly.  By  providing  the  opera  glass 
with  a  scale  it  may,  therefore,  be  used  as  an  optometer. — So 
also  may  the  telescope,  the  use  of  which  was  proposed  by  Hirsch- 
berg. 

Among  all  these  optometers  I  shall  mention  specially  only 
that  of  Badal,  on  account  of  its  admirable  principle.  It  is  com- 
posed of  a  single  convex  lens,  the  focus  of  which  coincides  with 
the  anterior  nodal  point  of  the  eye.  The  position  of  the  latter 


ANOMALIES   OF  REFRACTION,  //-  KVl; 

is  made  secure  by  an  eye-rest.  A1  diminished  copy  of  the  chart 
of  Snellen  is  placed  on  the  other  side  of  the  lens,  movable  for- 
wards and  backwards.  By  displacing  the  object  we  can  make 


Fig.  58. — Principle  of  Badal. 

i 

the  image  appear  anywhere,  and  it  is  easy  to  see  (fig.  58)  that 

the   retinal    image    remains   always   the   same   size,    no   matter 
whether  the  object  is  at  bb  or  at  aa,  etc.     We  can  therefore 


Fig.  59. 


measure  the  visual  acuity  with  this  optometer.  The  same  result 
is  obtained  by  making  the  focus  of  the  lens  coincide  with  the 
anterior  focus  of  the  eye  (fig.  59). 

45.  Myopia. — There  exist  two  forms  of  axial  myopia,  one 
which  depends  on  near  work,  and  one  which  does  not.  (i) — 
Myopia  from  near  work  appears  usually  at  an  age  ranging  from 
6  to  15  years;  it  often  stops  at  the  age  of  25  years.  It  attains 
medium  degrees  and  does  not  seem  to  exceed  the  limit  of  9  D. 
Complications,  except  staphyloma,  are  rare. 


(1)  Even  eliminating  these  two  forms  of  myopia,  it  is  probable  tnat  there  would 
still  remain  a  certain  number,  due  to  a  congenial  disagreement  between  the  optic 
system  and  the  length  of  the  axis  of  the  eye,  for  it  is  not  probable  that  all 
normal  eyes  are  constructed  so  as  to  be  exactly  emmetropic.. — But  myopia  between 
2  D.  and  9  D.  is  so  rare  among  uneducated  persons,  that  this  third  form  must 
comprise  only  light  degrees. 


PHYSIOLOGIC  OPTICS 


Dangerous  myopia  is  sometimes  congenial  and  stationary;  as 
a  rule  it  develops  in  early  infancy,  and  continues  to  increase 
during  the  whole  life.  At  the  age  of  20  years  it  generally  ex- 
ceeds 9  D.  This  form  of  myopia  is  to  be  considered  as  a  malig- 
nant choroiditis,  and  it  is  to  it  that  dangerous  complications  of 
myopia  belong;  like  most  choroidal  affections  it  seems  to  be  a 
little  more  prevalent  among  women. 

In  1882  and  1883  I  examined  about  7,000  young  Danish  con- 
scripts, by  determining  their  refraction  by  means  of  the  upright 
image.  The  influence  of  near  work  is  seen  in  the  tallowing  list : 

Myopes. 

Students 32  per  cent. 

Persons  employed  in  offices  and  in  trade..  16      — 

Artists,    etc 13      — 

Tailor,  shoemakers,  etc 12      — 

(  Workmen    (hard  labor) 5  per  cent. 

"\  Agriculturists    (peasants) 2      — 

We  see  that  the  very  great  frequency  of  myopia  in  the  edu- 
cated classes  comprises  only  the  lowest  degrees.  The  very  high 
degrees  are  rather  more  frequent  in  the  illiterate  (fig.  60). — 
Among  the  peasants  I  have  even  met  more  cases  of  myopia 
greater  than  9  D.  than  of  myopia  between  2  D.  and  9  D. 

It  is,  therefore,  a  great  exaggeration  to  regard  myopra  from 
near  work  as  a  public  calamity,  as  is  done  especially  in  Germany. 
One  exaggeration  leads  to  another.  It  was  thought  formerly 
that  myopic  eyes  were  stronger  than  others  because  they  did 
not  become  presbyopic.  After  the  discovery  of  the  ophthalmo- 
scope very  grave  complications  in  cases  of  strong  myopia  were 
continually  met  with,  and  thus  originated  the  idea  expressed  in 
the  celebrated  phrase  of  Donders,  "I  do  not  hesitate  to  declare 
that  every  myopic  eye  is  a  diseased  eye,"  a  phrase  which  Cohn 
adopted  as  his  motto  in  the  first  of  the  great  compilations  of 
statistics  of  school  children  ever  made.  Later,  many  others  were 
made,  but  without  important  results.  They  show  conclusively 
that  myopia  is  more  frequent  and  more  pronounced  in  the  higher 
classes  of  the  schools;  but  as  the  pupils  of  these  classes  are 
older,  and  as  the  myopia  is  a  condition  that  develops  with  age, 


ANOMALIES  OF  EEFEACTION  IC3 

these  statistics  do  not  establish  definitely  the  influence  of  near 
work. 

The  distribution  of  the  two  forms  of  myopia  in  the  two  groups 
was  the  following: 


I 
II 


soil 


In  all.  Myopes  <  9  D. 

2.336         407  (17  per  cent.) 
5,187         169  (  a       —        ) 


Myopes  >  9  D. 
13   (0.56  per  -cent.) 
38  (0.73       —        ; 


Hyper-  8       6 
metropia 9       7 


Tig.  60. — Distribution  of  the  anomalies  of  refraction  among  the  young 

population  of  Copenhagen. 
Educated.  .  Uneducated. 


A  satisfactory  explanation  of  the  mechanism  by  which  near 
work  produces  myopia  has  not  yet  been  given.    Danders  named 


104  '    PHYSIOLOGIC  OPTICS 

three  factors :  first,  the  inclined  position  of  the  head  which  pro- 
duces hyperemia  of  the  globe  with  a  tendency  to  distentiom; 
second,  the  fatigue  of  the  eyes,  which  would  be  the  result  of 
prolonged  reading,  and  which  would  also  produce  hyperemia; 
third,  the  compression  which  the  external  muscles  would  exercise 
on  the  eye,  during  convergence  for  a  near  point. — Arlt,  who,  by 
his  autopsies,  proved  for  the  first  time  in  1854  that  myopia  is 
due  to  a  lengthening  of  the  globe,  laid  special  stress  on  the  action 
of  the  superior  oblique  while  reading.  The  eye  being  directed 
downwards,  this  muscle  may,  indeed,  compress  one  of  the  veins 
and  thus  produce  the  development  of  hyperemia.  Stilling  tried 
to  further  develop  this  theory  by  finding  the  predisposition  to 
myopia  in  a  special  form  of  the  orbit  (very  low — Hypoconchia) 
which  would  give  to  the  muscle  a  direction  more  likely  to  com- 
press the  eye. 

In  spite  of  the  slight  degree  of  accommodation  which  myopes 
need  (i),  the  theory  of  the  accommodative  origin  of  myopia  has, 
however,  many  believers,  and  I  think  they  are  right;  but  as  the 
mechanism  of  accommodation  was  scarcely  known  until  recent 
times;  it  is  not  wonderful  that  the  solution  of  the  problem  of 
myopia  from  near  work  was  sought  in  vain. 

46.  Selection  of  Spectacles. — Although  myopia  from  near  work 
is  not  to  be  considered  as  a  true  diseased  condition  of  the  eye, 
it  always  causes  a  disagreeable  feeling  which  it  is  our  duty  to 
prevent  as  much  as  possible.  As  it  is  near  work  which  produces 
myopia,  young  myopes  must  be  made  to  work  at  as  great  a  dis- 
tance as  possible;  and,  on  account  of  the  probable  influence  of 


(1)  It  is  possible  that  myopes  often  accommodate  more  than  we  think.  In 
low  degrees  they  frequently  work  within  their  far  point,  because  by  bringing  the 
work  near  they  can  see  more  detail.  As  to  high  degrees,  other  circumstances 
may  bring  about  a  quite  remarkable  accommodation.  This  is  why  Javal  said 
that  a  myopic  eye  may  be  focused  at  once  for  the  extremities  and  the  middle 
of  a  line  of  a  book.  If  the  myopia  is  10  D.,  the  length  of  the  line  is  10  cm., 
and  if  the  ends  of  the  line  are  seen  distinctly  without  accommodation,  the 
patient  is  obliged  to  accommodate  about  two  dioptries  when  reading  the  middle, 
unless  he  keeps  the  book  or  his  head  in  continuous  motion,  or  contents  himselt 
with  seeing  diffusely  a  part  of  the  line. 


ANOMALIES  OF  REFRACTION  105 

accommodation,  we  must  suppress  the  latter  as  much  as  possible, 
or  annul  it. — We  are  very  frequently  consulted  on  the  question 
of  glasses  by  parents  who  are  worried  at  seeing  their  children 
become  myopes. — If  the  myopia  is  low,  under  three  dioptrics,  we 
give  correcting  glasses  for  distant  vision,  and  nothing  for  near 
vision,  ( i )  recommending  the  patient  to  be  careful  as  to  the  dis- 
tance of  the  book  while  reading.  We  place  the  normal  distance 
for  work  at  33  centimeters. — If  the  myopia  exceeds  three 
dioptrics  we  give  for  near  vision  correcting  glasses  diminished 
by  3  D.  For  example,  if  the  myopia  is  6  D.  we  give  3  D.  for 
near  vision.  For  distant  vision  we  may  give  correcting  glasses 
or  a  supplementary  glass  to  superimpose  on  the  spectacles. — But, 
in  giving  concave  glasses  for  near  vision  we  must  forcibly  im- 
press upon  myopes  the  necessity  of  observing  the  minimum  dis- 
tance of  33  centimeters  when  working;  otherwise  the  glasses 
would  be  rather  harmful  by  superinducing  an  effort  of  accommo- 
dation which  might  cause  the  myopia  to  increase. 

When  the  myopia  exceeds  9  D.,  it  becomes  necessary  to  re- 
gard it  as  dangerous,  and  great  care  in  the  use  of  the  eyes  must 
be  recommended.  Generally  it  is  preferable  not  to  completely 
correct  myopia,  but  only  sufficiently  so  that  the  patient  may  not 
be  too  much  annoyed  in  moving  around.  As  the  acuity  is  fre- 
quently diminished  we  can  no  longer  insist  on  as  great  a  distance 
for  near  work;  thus  we  may  give  correcting  glasses  diminished 
by  4  to  5  D.  for  near  work,  which  places  the  far  point  at  25  or 
20  centimeters  respectively. — The  patient  must  be  advised  never 
to  work  with  his  head  lowered ;  in  the  latter  case  where  the  dis- 
tance of  the  work  is  20  cm.  a  desk  must  be  used. — Patients  fre- 
quently ask  us  for  advice  as  to  illumination.  Nb  artificial  light, 
except  an  arc  lamp,  is  hurtful  to  the  eyes;  the  stronger  it  is  the 
better,  because  artificial  illumination  never  attains  the  degree 
of  illumination  of  a  bright  day;  but  it  may  be  useful  to  protect 
the  eyes  with  a  shade. 


(1)  [In  the  United  States  we"  prefer  to  let  these  myopic  patients  wear  their 
glasses  constantly,  especially  as  these  eyes  are  usually  more  or  less  astigmatic. 
The  sucess  of  this  method  is  proved  by  the  careful  investigations  of  Dr.  S.  D. 
Risley.  See  his  article  on  School  Hjfgiene  in  the  System  of  Diseases  of  the 
Eye  by  Norris  and  Oliver,  Philadelphia,  1897.] — W. 


106  PHYSIOLOGIC  OPTICS 

When  the  myopia  is  very  high,  spectacles  are  frequently  of 
no  service,  as  the  patients  do  not  accept  them.  It  is  then  neces- 
sary to  restrict  near  work  as  much  as  possible.  For  distant 
vision  a  small  telescope  sometimes  gives  good  service.  In  order 
to  obviate  the  necessity  of  accommodation,  patients  should  be 
advised  to  lengthen  it  as  much  as  possible. 

47.  Treatment  of  Myopia.— Each  of  the  two  theories  by  which 
myopia  from  near  work  has  been  explained  has  given  rise  to 
a  treatment  of  this  defect.  The  theory  of  convergence  led  to  the 
attempt  to  stay  the  progress  of  myopia  by  performing  a  tenotomy 
of  the  external  rectus  as  soon  as  there  was  a  slightly  pronounced 
latent  divergent  strabismus  (which  was  called  insufficiency  of 
the  internal  recti — exopkoria,).  Certain  surgeons  performed 
thousands  of  operations  of  this  character:  the  result  was  very 
doubtful,  and  we  may  consider  this  operation  as  abandoned. 
The  theory  of  accommodation  led  to  treatment  by  atropine ;  but, 
before  speaking  on  this  subject,  I  shall  say  a  few  words  on  the 
use  of  atropine  for  the  determination  of  refraction,  a  method 
which  is  still  very  much  in  vogue  in  some  countries. 

De  Wecker  held  decided  views  on  the  abuse  o'f  atropine  in 
ophthalmic  practice,  and,  as  far  as  its  use  for  the  determination 
of  refraction  is  concerned,  I  am  in  perfect  agreement  with  him. 
— We  know  that  young  hypermetropes  are  accustomed  to  correct 
part  of  their  hypermetropia  by  using  their  accommodation,  and 
that  they  cannot  relax  this  accommodation  without  becoming 
trained  to  it  by  means  of  convex  glasses,  at  least  as  long  as  they 
fix  a  specified  object.  To  make  all  the  hypermetropia  manifest 
we  must  instill  atropine  in  order  to  paralyze  the  accommodation. 
It  is  this  perfectly  correct  observation  which  gave  rise  to  the 
idea  that  generally  a  better  determination  of  refraction  would 
be  obtained  by  using  atropine,  and  which  resulted  in  the  ciliary 
muscle  being  held  responsible  every  time  a  difference  of  re- 
fraction before  and  after  the  instillation  of  atropine  was  found. 
By  putting  atropine  in  the  emmetropic  eye  we  often  find  a  light 
degree  of  hypermetropia,  which  Danders  was  wont  to  explain  by 
assuming  a  "tonus  of  the  ciliary  muscle."  Frequently  also  we 


ANOMALIES  OF  REFRACTION  107 

see  myopia  diminish  slightly  under  the  influence  of  atropine,  and 
this  diminution  has  been  attributed  to  the  existence  of  a  "spasm 
of  accommodation,"  which  would  disappear  as  soon  as  the  ac- 
commodative muscle  would  be  paralyzed. 

These  errors  originated  in  the  belief  that  refraction  must 
necessarily  be  the  same  in  the  whole  pupillary  space.  It  is 
nothing  of  the  kind :  there  nearly  always  exist  differences  which 
are  frequently  very  considerable.  Thus  there  is  in  my  eye  a 
relatively  great  difference,  nearly  4  D.,  between  the  upper  border 
and  the  lower  border  of  the  pupil  (see  page  173). — When  we 
instil  atropine,  the  pupil  is  dilated  and  the  basilar  position  ot 
the  cornea,  which  is  much  flattened,  comes  into  play.  As  the 
flattening  of  these  parts  is  often  considerable  enough  to  over- 
correct  the  spherical  aberration,  we  find  that  the  refraction 
of  these  peripheral  parts  is  generally  less  than  that  of  the  central 
parts.  A  quite  slight  dilation  of  the  pupil  suffices  in  order  that 
the  area  of  these  parts,  which,  in  ordinary  conditions,  are  ex- 
cluded, may  be  greater  than  that  of  the  ordinary  pupil;  it  is 
this  fact  which  makes  us  judge  specially  by  them  in  the  deter- 
mination of  refraction.  If  the  peripheral  flattening  of  the 
cornea  is  less,  or  if  the  extent  of  the  optic  part  exceeds  the 
ordinary  limits,  which  sometimes  happens,  we  may,  thanks  to 
the  spherical  aberration,  obtain  an  increase  of  refraction  by 
instilling  atropine.  Such  cases  have  been  observed  among  others 
by  Javal;  they  were  very  difficult  to  explain  with  the  ideas  which 
have  been  held  on  the  subject  up  to  the  present,  since  it  could 
not  be  supposed  that  the  use  of  atropine  could  cause  a  spasm 
of  the  accommodation.  We  observe  like  phenomena  with  photo- 
graphic objectives  the  aberration  of  which  is  not  well  corrected ; 
the  focus  changes  on  changing  the  aperture  of  the  diaphragm. — 
Except  in  cases  of  latent  hypermetropia,  we  obtain,  therefore, 
generally  a  better  idea  of  ocular  refraction  by  the  ordinary  ex- 
amination without  atropine. 

Atropine  treatment  has  been  used  in  cases  of  progressive 
myopia;  the  ciliary  muscle  would  be  kept  paralyzed  for  15  days 
or  a  month,  in  order  to  arrest  the  progress  of  the  myopia,  the 


108  PHYSIOLOGIC  OPTICS 

special  purpose  being  to  counteract  the  spasm  of  accommodation, 
which  was  supposed  to  be  the  cause  of  the  progress  of  the 
myopia.  This  treatment  does  not  seem  to  have  been  effective. — 
In  cases  where  the  eyes  are  exposed  to  great  danger,  for  ex- 
ample in  detachment  of  the  retina,  it  may,  however,  be  useful 
to  procure  for  them  complete  rest  by  instilling  atropine  and  for- 
bidding work  altogether  for  some  time. 

Some  years  ago,  on  the  advice  of  Fukala,  the  profession  began 
to  treat  high  degrees  of  myopia  by  removing  the  crystalline 
lens,  generally  by  a  discission  followed  by  extraction.  This 
treatment,  which  Bonders  pronounced  criminal  at  a  time  when 
surgical  operations  were  more  dangerous  than  now,  often  seems 
to  give  very  good  results,  not  only  because  those  operated  on  be- 
come emmetropic  or  nearly  so  after  the  operation,  but  also  be- 
cause they  gain  considerably  in  visual  acuity  for  distance.  We 
have  already  seen  that  the  size  of  the  retinal  image  of  the  myopic 
eye,  corrected  by  a  glass  placed  at  the  anterior  focus,  fs  equal  to 
the  image  of  the  emmetropic  eye.  Niow,  in  the  emmetropic  eye 
the  retina  is  situated  about  16  millimeters  behind  the  posterior 
nodal  point;  in  a  myopic  eye,  which  has  become  emmetropic  by 
the  extraction  of  the  crystalline  lens,  the  retina  is  situated  at  the 
posterior  focus  of  the  cornea  or  about  24  millimeters  from  the 
nodal  point.  As  the  size  of  the  image  depends  only  on  this 
distance,  we  see  that  the  linear  enlargement  of  the  image  by  the 
operation  is  about  a  half.  Often  it  gains  still  more  because  the 
correcting  glass  is  placed  not  at  the  anterior  focus  but  a  little 
in  front,  which  has  the  effect  of  diminishing  the  image.  The 
loss  of  accommodation,  which  is,  indeed,  of  very  little  use  to 
myopes  of  a  high  degree,  cannot  counterbalance  these  advan- 
tages; nevertheless  there  is  reason  for  prudence  in  recommend- 
ing this  operation,  for  it  is  not  without  danger.  When  making 
the  discission  (followed  by  paracentesis)  we  may  fear  glauco- 
matous  complications  or  iridocylitis  as  a  consequence  of  a  too 
great  swelling  of  the  crystalline  lens.  If  extraction  is  performed 
an  accidental  loss  of  the  vitreous  body  may  sooner  or  later  pro- 
duce a  detachment  of  the  retina. 


ANOMALIES  OF  EEFEACT10N  109 

48.  Hypermetropia. — The  hypermetropic  eye  is  too  short.  The 
retina  being  too  near  the  optic  system,  the  hypermetrope  cannot, 
without  an  effort  of  accommodation.,  reunite  on  the  retina  parallel 
or  diverging  rays.  When  the  hypermetropia  is  high,  the  ampli- 
tude of  accommodation  diminishing  with  age,  there  comes  a 
time  when  the  patient  can  no  longer  correct  his  hypermetropia 
by  accommodation  (absolute  hypermetropia). — The  degree  ot 
hypermetropia  is  expressed  by  the  strongest  convex  glasses  with 
which  the  patient  can  distinguish  distant  objects  distinctly.  To 
disclose  all  the  hypermetropia,  it  is  often  necessary  to  paralyze 
the  ciliary  muscle  by  means  of  atropine,  because  the  patient  has 
formed  the  habit  of  accommodating  as  soon  as  he  fixes  an  object, 
and  he  cannot  suddenly  rid  himself  of  this  habit  even  when  we 
put  before  his  eye  a  convex  glass  which  should  eliminate  any 
necessity  of  accommodation. — That  part  of  hypermetropia  which 
we  cannot  make  manifest  by  the  ordinary  examination  is  called 
latent  hypermetropia  (Donders);  it  diminishes  with  age,  and  it 
need  not  be  regarded  as  a  very  definite  quantity.  We  can  often, 
by  working  a  little  with  the  patient,  make  him  accept  stronger 
and  stronger  glasses.  In  the  dark  room  where  the  patient  does 
not  fix,  hypermetropia  frequently  becomes  manifest  in  its  entirety 
which  permits  it  to  be  determined  with  the  refraction  ophthal- 
moscope or  by  skiascopy. 

ACCOMMODATIVE  ASTHENOPIA. — The  hypermetrope,  being 
obliged  to  use  part  of  his  accommodation  to  neutralize  his  defect 
of  refraction,  generally  becomes  fatigued  more  quickly  than  the 
emmetrope  by  near  work.  The  essential  symptom  of  this  accom- 
modative asthenopia  is  that,  while  reading,  the  letters  become 
blurred.  Wrhen  this  symptom  appears,  the  patient  reads  with 
ease  for  some  time;  then  the  letters  begin  to  become  indistinct, 
so  that  he  is  forced  to  rest  a  while.  If  he  begins  again  he  gets 
along  well  for  a  shorter  time  than  before,  after  which  the  same 
phenomenon  is  reproduced.  If  the  patient  still  continues  there 
supervene  fatigue,  orbital  pains,  etc.;  but  these  phenomena  are 
secondary,  and  we  must  not,  from  their  appearance,  decide  on 
hypermetropia  as  the  cause  in  the  absence  of  the  essential 


110  PHYSIOLOGIC  OPTICS 

symptom,  viz.,  the  indistinctness  of  the  letters  after  reading 
for  some  time.  We  need  no  longer  attribtue  the  complaints  of 
patients  to  a  low  degree  of  hypermetropia.  Low  degrees  of 
hypermetropia  manifest  themselves,  as  a  rule,  only  by  the  pre- 
mature appearance  of  presbyopia.  We  may  easily  correct  a 
low  degree  of  hypermetropia,  even  in  young  people,  but  we 
must  not  expect  to  obtain  great  results.  The  complaints  of  the 
patients  have  generally  other  causes. 

Boehm,  Stellwag  and  others  recommended  the  use  of  convex 
glasses  in  cases  of  accommodative  asthenopia,  but  to  Bonders 
belongs  the  credit  of  having  brought  them  into  general  use.  His 
labors,  indeed,  contributed  greatly  to  dispel  the  fear  which 
earlier  oculists  had  of  strong  convex  glasses.  They  considered 
asthenopia  as  the  forerunner  of  amblyopia,  and  believed  that  the 
giving  of  convex  glasses  was  conducive  to  the  development  of 
the  latter. 

Hypermetropes  generally  prefer  a  great  distance  tor  work 
in  order  not  to  fatigue  their  accommodation.  But,  when  the 
hypermetropia  is  very  high,  which  demands  an  effort  of  accom- 
modation much  too  fatiguing,  we  see  patients  choose  a  very 
short  distance,  moving  the  book  to  within  a  few  centimeters 
from  the  eyes.  They  see  better,  thanks  to  the  considerable  en- 
largement of  the  retinal  images.  It  is  true  that  they  are  blurred ; 
but,  on  bringing  the  object  nearer,  the  circles  of  diffusion  in- 
crease less  quickly  than  the  images,  and  moreover,  the  patients 
can  diminish  them  by  winking  their  eyelids. 

The  rule  of  Donders  for  the  selection  of  spectacles  was  to 
correct  the  manifest  hypermetropia  plus  one-fourth  of  the  latent, 
that  is  to  say,  to  give,  for  young  people,  convex  glasses  a  little 
stronger  than  those  which  they  accept  for  distant  vision.  I 
consider  this  rule  a  wise  one;  others  correct  all  the  hyper- 
metropia. Generally  the  patients  are  dissatisfied  at  the  begin- 
ning, before  becoming  accustomed  to  the  spectacles;  the  glasses 
annoy  them,  and  it  is  advisable  to  forewarn  them  that  they  will 
do  so  for  some  time.  This  annoyance  is  greater  the  stronger 


ANOMALIES  OF  EEFEACT10N  111 

the  glasses,  which  is  one  reason  for  not  correcting  all  the  hyper- 
metropia.  Another  reason  is  that  patients  are  much  more  an- 
noyed when,  for  one  reason  or  another,  they  cannot  wear  the 
glasses,  since  they  have  lost  the  habit  of  overcoming  their  hyper- 
metropia  by  accommodation. 

If  the  hypermetropia  is  low  or  medium  (i  to  3  D.)  there  is 
no  reason  for  giving  glasses  for  distant  vision,  at  least  to  young 
people  who  easily  correct  their  hypermetropia  by  accommo- 
dating; we  may  leave  them  free  in  this  regard.  If  the  hyper- 
metropia is  high  or  if  there  is  a  tendency  to  strabismus,  the 
glasses  must  be  worn  constantly,  (i) 

49.  Aphakia. — It  is  very  rare  to  find  true  hypermetropia 
which  exceeds  7  D.  (see  fig.  60).  The  higher  degrees  are  met 
with  only  in  aphakia  (absence  of  the  crystalline  lens). 

The  degree  of  hypermetropia  of  the  aphakic  eye  can  be  calcu- 
lated by  means  of  the  formula  JL1  -f  ?|  =i.  With  the  values 
of  the  simplified  eye  we  have  F1=2^,  F2=32,  f  2=24.7,  which 
gives  f1=Si.2.  The  far  point  is  therefore  situated  at  81.2 
mm.  behind  the  cornea;  the  eye  will  be  corrected  by  a  convex 
glass  of  96  millimeters  =10.4  D.,  placed  at  15  millimeters  in 
front  of  the  cornea.  We  find,  in  fact,  that  nearly  all  the  em- 
metropes  operated  on  for  cataract  are  corrected  with  a  glass 
of  from  10  to  ii  dioptrics. 

But  it  would  be  an  error  to  apply  this  number  to  the  ametro- 
pias,  and  to  think  that  we  could  always  find  the  post-operation 
refraction  by  diminishing  the  ante-operation  refraction  by  n  U. 
To  find  the  correcting  glass  for  ametropias  we  must  calculate 


(1)  [In  this  country  our  reasoning  upon  this  point  is  quite  different.  As 
people  with  hypermetropia,  higher  than  3  D.,  accommodate  with  great  difficulty, 
they  do  not  keep  it  up  very  long  at  a  time  or  sometimes  avoid  to  correct  accom- 
modation by  reading  very  near  with  diffuse  but  enlarged  images  ab  has  been  so 
well  explained  by  the  author.  They  thus  frequently  rest  their  eyes  more  than 
the  persons  with  lower  degrees  of  H.  who  use  their  accommodation  more  con- 
stantly and  on  that  account  show  more  asthenopia.  At  any  rate  the  constant 
correction  of  the  lower  degrees  of  hypermetropia  has  relieved  many  cases  of 
obstinate  asthenopia.] — W. 


112 


PHYSIOLOGIC  OPTICS 


it  in  the  same  way  as   for  emmetropes.     It  is  thus  that  Dr. 
Stadfeldt  has  calculated  the  following  little  table: 


Before  )  H  7 
operation  j 

H.  5 

H.  3 

H.  1 

E 

M.  1 

M.  3 

M.  5 

M.  7 

After  I  TT  IK 
operation  j  J 

H.13.8 

H.12.5 

H.11.3 

H.10.6 

H.10.1 

H.8.9. 

H.  7.8 

H.  6.6 

BeforC  I  M.  9 
°Peration  j 

M.  11 

M.  13 

M.  15 

M.  17 

M.  19 

M.  21 

M.  23 

M.  25 

After  1  TT  K  r 
operation  J  H'5'5 

H.4.4 

H    3.4 

H.  2.3 

H.  1.3 

H.  0.2 

M.  0.8 

M.  1.8 

M.  2,7 

Comparing  this  table  with  the  following  table  which  has  been 
made  up  from  a  series  of  results  from  operations  published  by 
Pflueger,  we  see  that  the  agreement  is  sufficiently  satisfactory. 

Before  oper.  M 10  Mil  M 12  M 13  M 14  M 15  M 16  M 18  M  22 
After  —  H  5  H5.5  H3.5  H3.5  H3.5  H  1  H2.5  M  2  M  2 

Dimmer  has  directed  attention  to  a  slight  source  of  error  in 
the  ordinary  examination  of  aphakics.  The  lenses  of  our  test 
cases  are  biconvex,,  while  those  which  the  optician  makes  for 
patients  are  generally  sphero-cylindrical,  the  cylindrical  surface 
being  turned  towards  the  eye.  Now,  the  optic  center  of  biconvex 
lenses  is  situated  at  the  middle  of  the  lens,  while  that  of  plano- 
convex glasses  is  situated  at  the  apex  of  the  convex  surface. 
It  follows  that  the  spherical  effect  of  the  sphero-cylindrical  glass 
is  a  little  greater  than  that  of  the  biconvex  glass,  having  the 
same  focal  distance,  the  posterior  focus  being  situated  a  little 
nearer  the  glass  in  the  former  case.  The  error  may  reach  a 
half  dioptry.  For  some  time  test  cases  have  been  manufactured 
in  Austria  in  which  the  strong  convex  glasses  are  plain  on 
one  side. 

Ostwalt  has  laid  stress  on  the  influence  which  the  distance  ot 
the  glass  from  the  eye  exerts  on  the  power  of  sphero-cylindrical 
glasses.  Supposing,  for  example,  that  an  eye  is  corrected  by 
-|-ii  D.  with  -j-3  D.  cyl.,  placed  at  15  millimeters  in  front  ot 
the  eye.  Such  a  glass  has,  in  one  of  the  principal  meridians,  a 


ANOMALIES  OF  EEFEACTION  113 

focal  distance  of  91  millimeters,  in  the  other  of  71  millimeters. 
The  far  point  of  the  eye  is  thus  found  in  one  of  the  meridians 
at  91  mm. — 15  mm.=76  mm.  (13.1  D.),  in  the  other  at  71  mm. 
— 15  mm. =56  mm.  (17.9  D.).  Its  astigmatism  is,  therefore, 
really  4.8  D.  and  not  3  D.  As  far  as  the  subjective  examina- 
tion is  concerned  this  difference  plays  no  part,  since  the  glasses 
with  which  we  examine  our  patients  are  at  the  same  distance 
from  the  eye  as  those  which  the  patient  will  wear,  but  it  is  not 
so  with  the  ophthalmometer,  which  tells  the  true  astigmatism 
of  the  eye;  we  must  recollect,  therefore,  that  in  this  case  the 
number  furnished  by  the  ophthalmometer  is  higher  than  that 
which  suits  the  patient. — In  the  case  of  simple  cylindrical  glasses 
the  same  influence  makes  itself  felt,  but  to  a  much  less  extent ; 
a  convex  cylinder  of  6  D.  thus  corresponds  with  a  true  astigma- 
tism of  6.5  D.,  a  concave  cylinder  of  6  D.  with  5.5  D. 

Bibliography. — Bonders  (F.  C.).  On  the  Anomalies  of  Accommodation 
and  Ee  fraction  of  the  Eye.  London,  1864. — Mauthner  (L.).  Vorlesungen 
uber  die  optischen  Fehler  des  Auges.  Wien,  1876. — Landolt  (E.).  .La 
refraction  et  r accommodation  de  Voeil  in  Wecker  and  Landolt.  Traite 
complet  d'ophthalmologie.  Paris,  1883. — Boehm  (L.).  Das  Schielen. 
Berlin,  1845. — Arlt  (F.).  Die  Krdrikheiten  des  Auges,  I-III.  Prag.,  1851. 
— Stellwag  v.  Carion.  Die  Ophthalmologie  vom  naturwissenschaftlichen 
Standpunlcte  aus.  I-II.  Erlangen,  1853. — Tscherning  (M.).  Studien  uber 
die  Aetiologie  der  Myopie.  Arch.  f.  Opth.,  XXIX,  I,  1883. — Dimmer  (F.). 
Zur  Glaesercorrection  bei  AphaMe.  Kl.  M.  f.  A.  1891. — Ostwalt  (F.). 
Einige  Worte  uber  Glasercorrection  bei  AphaTcie.  Kl.  M.  f.  A.  1891. — 
Demlcheri  (L.).  Faux  lenticone.  Ann.  d'oc.  1895. 


CHAPTER  VII 
SPHERICAL  ABERRATION 

50.  Optic  Principles. — When  the  aperture  of  a  spherical  lens 
is  not  very  small,  the  rays  proceeding  from  a  point  of  the  object 
do  not,  after  refraction,  reunite  exactly  at  a  point,  as  would  be 
essential  to  form  a  good  image ;  the  borders  of  the  lens  are  more 
refracting  than  the  center.  Thus  the  test  case  lens,  the  center 
of  which  has  a  refraction  of  20  D.,  refracts  25  D.  towards  the 
borders.  Generally  speaking,  the  same  is  true  of  all  refracting 
and  reflecting  systems  (fig.  61).  It  is  possible,  nevertheless,  to 


Fig.  61. — Refraction  of  a  pencil  of  parallel  rays  by  a  spherical  surface. 
Spherical  aberration.  At  A,  the  rays  are  condensed  towards  the 
border;  at  B,  towards  the  axis  of  the  pencil;  p,  q,  two  needles. 

construct  systems  of  large  aperture,  which  present  only  very 
little  aberration  (aplanatic  lenses),  and  others  in  which  the 
aberration  is  over-corrected,  the  borders  being  less  refracting 
than  the  center  (Icntilles  suraplanctisees). 

The  degree  of  aberration  increases  as  the  square  of  the  aper- 
ture of  the  lens  and  as  the  cube  of  its  refracting  power.  It  de- 
pends, besides,  on  the  distance  of  the  object  and  the  form  of  the 
lens.  A  plano-convex  lens  presents  less  aberration  than  a  bi- 
convex lens,  if  the  spherical  side  is  turned  towards  the  incident 
rays  supposed  to  be  parallel ;  it  presents  more  in  the  contrary 
direction.  It  is  for  this  reason  that  the  objectives  of  opera 

114 


SPHERICAL  ABERRATION  115 

glasses  are  bulged  in  front.  The  best  form  of  simple  lens  is 
that  which  the  English  call  crossed  lens  (periscopic),  in  which 
the  radius  of  the  posterior  surface  is  about  six  times  greater 
than  that  of  the  anterior  surface.  We  give  here  the  refracting 
power,  at  15  millimeters  from  the  axis,  of  different  lenses,  all 
having  at  the  middle  a  refraction  of  20  D.  The  incident  rays  are 
supposed  to  be  parallel. 

Crossed  lens.     Plano-convex  with  the     Bi-convex.     Plano-convex  with  the 
convex  surface  in  front.  plane  surface  in  front. 

21.1  D.  22.3  D.  23.6  D.  23.8  D. 

It  is  evident  that,  the  weaker  the  aberration  of  the  lens,  the 
more  aperture  can  be  given  to  it  without  the  aberration  inter- 
fering with  the  distinctness  of  the  image.  The  crossed  lens  is 
little  used,  because  the  plano-convex  lens  is  nearly  as  good. 
Besides,  for  the  correction  of  chromatic  aberration,  compound 
lenses  are  usually  employed  (a  flint  lens  and  a  crown  lens 
cemented  together).  Both  glasses  can  then  be  cut  in  such  a 
way  as  to  neutralize  the  spherical  aberration  also,  until  the  total 
aberration  becomes  almost  nothing  for  a  given  distance  of  the 
object. 

51.  Phenomena  Dependent  on  the  Spherical  Aberration  of  Lenses. 

— I  am  going  to  explain  some  experiments  by  which  the  spherical 
aberration  of  lenses  may  be  studied.  In  order  to  have  very 
marked  phenomena  we  must  use  a  strong  lens,  20  D.  (convex) 
of  the  test-case,  for  example,  or,  better  still,  a  strong  plano- 
convex lens  (the  objective  of  an  opera  glass),  the  plane  side 
of  which  is  turned  towards  the  luminous  source,  placed  at  a 
great  distance. 

a.  APPLICATION  OF  THE  PRINCIPLE  OF  SCHEINER. — We  place 
on  the  lens  an  opaque  screen  in  which  we  have  previously  made, 
not  two  apertures  as  in  the  experiment  of  Schemer,  but  four, 
which  are  equidistant,  placed  on  the  horizontal  diameter  of  the 
lens,  two  central  ones,  2  and  3,  and  two  peripheral,  I  and  4 
(fig.  62).  The  object  being  a  distant  luminous  source,  we  re- 
ceive the  images  on  a  white  screen  placed  behind  the  lens. 


116 


PHYSIOLOGIC  OPTICS 


First,  placing  the  latter  beyond  the  focus,  we  see  (fig.  62  A) 
four  luminous  spots  which  correspond  to  the  apertures  of  the 
screen,  but  which  are  placed  in  reverse  order.  The  distance  be- 


T 

r- 

"N 

T 

^ 

•1 

. 

; 

i 

,' 

1 

;• 

;; 

'• 

i 

i  , 

i 

'1 

h 

'; 

1 

i 

i 

'i 

4 

f         , 

: 

I 

i 

i 

? 

• 

>                   % 

G        1 

i 

*    1 

;  i 

1 

i 
o    < 

:    J 

1 

i                  « 

Fig.  62. — Spherical  aberration  of  a  lens. 

tween  the  central  spots  is  less  than  that  which  separates  each 
of  the  peripheral  spots  from  the  neighboring  spot.  The  two 
central  spots  reproduce  the  form  of  the  source  enlarged,  while 
the  two  peripheral  spots  are  elongated  in  the  horizontal  direction, 
especially  if  the  aberration  is  strong.  The  pencils  passing 


SPHERICAL  ABERRATION  117 

through  the  peripheral  openings  are,  indeed,  astigmatic  by  inci- 
dence (see  ch.  IX1).  By  moving  the  screen  nearer,  the  two 
central  spots  are  blended  into  one  (fig.  62  B).  At  this  moment 
the  screen  is  at  the  focus  of  the  central  part  of  the  lens,  while 
it  is  still  beyond  the  focus  of  the  peripheral  parts.  Advancing 
the  screen  still  more,  the  spots  i  and  4  approach  and  are  blended 
(fig.  62  E,  focus  of  the  peripheral  part),  while  spots  2  and  3 
are  again  separated.  Finally  we  have  four  spots,  as  at  the  begin- 
ning of  the  experiment;  but  they  are  now  arranged  in  the  same 
order  as  the  apertures;  the  distances  separating  the  two  spots 
on  each  side  are  less  than  the  distance  between  the  central  spots. 
We  observe  also  that  the  peripheral  spots  are  now  elongated  in 
the  vertical  direction. — If  the  lens  is  very  large  we  can  observe 
all  the  different  phases  shown  on  fig.  62. 

To  determine  the  degree  of  aberration,  we  have  only  to 
measure  the  distances  of  the  positions  E  ( focus  of  the  peripheral 
parts)  and  B  (focus  of  the  central  part)  from  the  screen.  The 
difference  between  these  two  distances,  expressed  in  dioptrics, 
tells  the  degree  of  aberration.  To  have  more  accurate  measure- 
ments it  is  advisable  to  cover,  each  time,  the  two  apertures  we 
are  not  using;  for  the  determination  of  E,  we  cover  the  central 
aperture,  for  that  of  B  the  peripheral  apertures. — We  can  also 
cover  the  two  apertures  situated  on  the  same  side  and  determine 
the  focal  distance  on  the  other  side  (the  position  F,  fig.  62), 
but  it  is  not  necessary  in  order  to  determine  the  course  of  the 
rays :  we  can,  indeed,  construct  figure  62  by  knowing  the  posi- 
tions B  and  E  only. 

b.  EXAMINATION  OF  THE  CIRCLES  OF  DIFFUSION. — Examining 
the  circle  of  diffusion,  without  putting  the  screen  with  the 
openings  on  the  lens,  we  see  that  as  long  as  the  white  screen 
is  situated  beyond  the  focus,  the  light  is  concentrated  at  the 
middle  of  the  circle;  the  brightness  diminishes  rapidly  towards 
the  borders.  When  it  is  situated  within  the  focus,  we  see,  on 
the  contrary,  a  luminous  disc  surrounded  by  a  more  brilliant 
circle.  This  phenomenon  is  easy  to  understand :  we  see,  in  fact, 
in  figure  62,  that  the  rays  are  condensed  towards  the  border, 


118 


PHYSIOLOGIC  OPTICS 


between  the  lens  and  the  focus,  while  they  are  concentrated 
around  the  axis  beyond  the  focus. 

c.  DEFORMITY  OF  THE  SHADOWS. — Put  the  white  screen  beyond 
the  focus,  and  place  a  knitting  needle  against  the  lens.  We  then 
see  the  shadow  of  the  needle  in  the  circle  of  diffusion  and  ob- 
serve that  this  shadow  is  straight  only  if  the  needle  coincides 


Fig.  63. — Deformation  of  the  shadows  of  the  needles.  Successive  sections 
of  the  pencil  of  figure  61.  Section  I  is  supposed  to  be  made  at  C 
(fig.  61),  section  II  at  A,  section  III  at  B,  the  two  latter  enlarged; 
ab,  a  needle;  a'  b'  and  a"  b",  its  shadows. 

with  a  diameter  of  the  lens ;  otherwise  it  is  curved,  with  its  con- 
vexity towards  the  center.  If  the  screen  is  between  the  focus 
and  the  lens,  the  shadow  is  concave  towards  the  middle,  but  the 
curvature  is  much  less  pronounced. 

To  understand  these  deformities  let  us  suppose  the  lens  divided 
into  concentric  zones  of  the  same  width.  A  glance  at  figure  62 
shows  that  after  refraction  the  corresponding  zones  of  the  circle 
of  diffusion  diminish  in  width  towards  the  periphery,  when  the 
screen  is  situated  between  the  focus  and  the  lens,  while  they 
increase  in  width  towards  the  periphery  beyond  the  focus.  In 
figure  63,  I  shows  the  lens  seen  from  the  front  and  divided  into 
concentric  circles;  the  two  straight  lines  represent  two  needles. 
In  figure  63,  II  represents  a  circle  of  diffusion  between  the  lens 
and  the  focus.  We  see  that  the  zones  become  narrower  towards 
the  edge,  and  we  understand  that  the  point  of  is  relatively  nearer 
the  center  than  the  point  b',  which  gives  the  shadow  its  curved 
form.  Knowing  the  position  of  the  concentric  circles  of  the 
diffusion  spots,  it  is  easy  to  construct  the  form  of  the  shadow, 


SPHERICAL  ABERRATION  119 

since  the  shadow  of  a  point  of  the  needle  must  be  at  the  same 
angular  distance  from  the  horizontal  diameter  as  the  point  itself. 
In  figure  63,  III  represents  a  circle  of  diffusion  beyond  the  focus. 

An  over-corrected  lens  gives  all  the  phenomena  here  men- 
tioned, but  in  the  reverse  order,  while  a  corrected  lens  (aplanatic) 
gives  none  of  them.  The  circles  of  diffusion  of  an  aplanatic 
lens  have  the  same  brightness  in  their  whole  extent,  and  the 
shadow  of  the  needle  remains  straight  everywhere.  To  give  a 
good  image  a  lens  must  be  approximately  aplanatic.  The  pre- 
ceding experiments  can  be  used  as  a  verification  of  the  aplanatism 
of  a  lens. 

d.  APPLICATION  OF  THE  PRINCIPLE  OF  FOUCAULT. — We  obtain 
very  pretty  phenomena  by  using  the  method  by  which  Foucault 
studied  his  telescopes.  We  place  a  luminous  point  a  little  beyond 
the  focus  of  the  lens  which  we  wish  to  study,  so  that  its  image 
is  quite  distant  (2  to  3  meters).  The  observer  takes  his  place 
beyond  this  image,  so  that  his  eye  is  in  the  luminous  pencil  on 
the  axis  of  the  lens,  which  he  approaches  gradually.  Under 
these  circumstances  the  eye  sees  luminous  the  parts  of  the  lens 
which  send  rays  to  it.  If  the  lens  were  aplanatic,  all  the  rays 
would  meet  at  the  focus,  and,  reaching  this  point,  the  observer 
ought  to  see  the  entire  lens  luminous.  At  some  distance  from 
the  focus,  he  would  see,  on  the  contrary,  only  a  small  central 
part  luminous,  the  other  rays  not  entering  his  eye.  If  the  lens 
is  affected  with  spherical  aberration,  we  observe  the  following 
phenomena :  placed  very  far  off  we  see  only  a  quite  small  central 
spot,  which  increases  in  diameter  accordingly  as  we  approach 
the  focus  where  it  attains  its  maximum;  but  even  here  it  is  far 
from  filling  the  entire  lens.  Approaching  still  nearer  we  see  a 
luminous  ring  become  detached  and  separated  from  the  central 
part  by  a  dark  zone.  This  ring  dilates  more  and  more  accord- 
ingly as  we  approach  the  lens,  while  the  dark  zone  becomes  en- 
larged. On  reaching  a  certain  point,  the  ring  extends  to  the 
borders  of  the  lens  and  disappears.  The  phenomena  are  still 
clearer  if  we  look  through  a  narrow  diaphragm. — It  is  easy  to 
account  for  the  nature  of  these  phenomena  by  glancing  at  figures 


120  PHYSIOLOGIC  OPTICS 

61  and  62.  Thus,  if  we  suppose  the  pupil  of  the  observer  re- 
duced to  a  point  and  placed  at  the  intersection  E,  fig.  62,  it 
would  receive  rays  I  and  4,  and  the  borders  of  the  lens  would 
appear  luminous,  while  the  parts  2  and  3  would  be  black,  the 
corresponding  rays  passing  to  one  side  of  the  pupil.  There  will 
always  be  a  small,  luminous  spot  at  the  middle,  since  the  axial 
ray  always  enters  the  eye.  The  distance,  in  dioptrics,  between 
the  place  where  the  ring  appears  and  that  where  it  disappears, 
tells  the  amount  of  the  aberration. — If  the  aberration  is  over- 
corrected  we  have  the  same  phenomena  in  the  reverse  order: 
placed  at  the  focus,  we  must  move  away  in  order  to  see  the  ring ; 
the  further  away  we  move  the  more  it  increases,  until  finally  it 
disappears. 

52.  Aberration  of  the  Human  Eye.    Experiments  of  Volkmann. 
— This  scientist  examined  the  aberration  of  the  eye  by  repeating 

the     experiment     o  f 

T7T  TttT      $ckeiner     with     four 

' '  ' '      openings  located  as  in- 

a/  bad,  «.• 

dicated  in  figure  64,  C. 
Looking  at  a  pin  placed 

*  tilt     TT     T    IT!     ITT!   bey°nd  the  far  p°int 

1111      through     these     open- 
ings, it  is  seen  quad- 
c  ;\  rupled  (fig.  64,  A,  a)  ; 

Fig.  64.— Experiment  of  VolTcmann.—a,  corre-  and  b7  moving  closer 
spends  to  the  most  distant  position ;  e,  to  the  to  it  he  observed  the 
nearest  position  of  the  needle.  A,  phenomena  different  phases  illus- 
observed  by  an  eye  with  strong  spherical  A  '  fi  £>  A 

aberration;  B,  by  an  eye  with  over-corrected   tratei1  m  ngure  04,  A, 
aberration.  in  the  order  in  which 

they  are  shown  in  the  figure,  and  which  corresponds  to  the  spher- 
ical aberration.  It  is  easy  to  account  for  this  phenomenon  by 
comparing  figure  64  with  figure  62.  In  the  position  b,  the  pin 
is  at  the  far  point  of  the  central  parts  of  the  pupil,  since  the  two 
central  images  are  reunited;  it  is  still  beyond  the  focus  of  the 
peripheral  parts  since  the  peripheral  images  are  not  yet  blended. 
Most  of  the  time,  the  persons  examined  observe  the  same  phe- 


SPHERICAL  ABERRATION  121 

nomena  in  the  same  order,  but  some  see  them  in  the  reverse 
order  (fig.  64,  B),  which  indicates  over-corrected  aberration.  In 
the  position  d  (fig.  64,  B)  the  pin  is  at  the  far  point  of  the 
central  parts  and  within  the  far  point  of  the  peripheral  parts. — 
It  is  probable  that  these  latter  persons  used  their  accommodation, 
for  it  is  quite  rare  to  find  over-corrected  aberration  in  an  eye 
in  a  state  of  repose;  I  have,  however,  met  instances,  especially 
among  persons  having  a  large  pupil.  On  the  contrary,  during 
accommodation,  it  is  the  rule  that  the  aberration  is  over-corrected, 
as  we  shall  see  later  on. 

53.  Experiments  of  Thomas  Young. — Long  before  Volkmann's 
time,  Young  had  already  performed  a  series  of  experiments  much 
more  conclusive,  but  which  had  been  forgotten. 

a.  A  myopic  eye  sees  a  distant  luminous  point  as  a  circle  of 
diffusion,  the  brightness  of  which  is  concentrated  at  the  middle, 
if  the  eye  has  spherical  aberration  (fig.  65,  I).  If  the  aberra- 
tion is  over-corrected,  or  if  the  luminous  point  is  inside  the  far 


I  II 

Fig.  65. — Distribution  of  the  light  of  the  circle  of  diffusion  in  an  eye  with 
strong  aberration  (Antonelli).  In  I  the  luminous  point  is  beyond; 
in  II  within  the  focus. 

point,  it  is  the  borders  that  are  the  more  luminous ;  an  aplanatic 
eye,  or  one  nearly  so,  sees  the  circle  of  a  uniform  brightness.  To 
repeat  the  experiment,  when  one  is  not  myopic,  one  places  in 


122 


PHYSIOLOGIC  OPTICS 


front  of  the  eye  a  convex  lens  of  3  to  4  dioptrics.  Many  eyes, 
the  optic  system  of  which  is  irregular,  perceive  eccentric  con- 
centrations of  the  light;  I  shall  return  to  this  immediately,  (i) 

b.  Bringing  a  needle  in  front  of  the 
eye,  made  myopic,  while  the  experiment 
a  is  being  performed,  we  see  the  shadow 
of  the  needle  in  the  circle  of  diffusion. 
If  the  shadow  remains  straight  every- 
where, there  is  no  perceptible  aberration ; 
if  it  is  curved,  its  concavity  towards  the 
periphery  indicates  ordinary  aberration; 
its  concavity  towards  the  center  indicates 


•y         •«    »*r^j  i/ 

Fig.  66. — The  aberroscope.    Fig.  67. — The  rules  of  the  optometer  of  Young. 


over-corrected  aberration.  We  can  perform  the  experiment  in 
the  different  meridians  and  thus  prove  that  the  aberration  is 
not  always  the  same  in  the  different  directions. 

I  have  constructed  a  little  instrument,  the  aberroscope    (fig. 
66),  consisting  of  a  plano-convex  lens  which,  on  its  plain  side, 


(1)  Young  does  not  mention  the  experiment  under  this  form,  but  it  is  a 
sequence  of  other  experiments  which  he  describes.  For  the  experiment  &,  he 
used  the  bars  separating  the  four  slits  of  his  optometer. 


SPHERICAL  ABERRATION 


123 


carries  a  micrometer  in  the  form  of  little  squares.  We  look  at  a 
distant  luminous  point  through  the  lens,  moving  it  10  or  20 
centimeters  from  the  eye  in  order  to  observe  whether  the  lines 
then  appear  curved  or  not. 

i 


o  o  o 

i  n  m 

Pig.  68. — I  and  II.  The  appearance  assumed  by  the  line  of  the  optometer 
of  Young,  seen  through  four  slits  by  one  eye  with  strong  spherical 
aberration.  O,  position  of  the  eye;  a  (a'}  far  point  of  the  peripheral 
parts;  6  (&')  far  point  of  the  central  parts. 

III.  The  appearance  of  the  line,  seen  in  the  same  circumstances 
by  one  eye  (left)  with  marked  obliquity.  The  external  part  of  the 
pupillary  space  is  more  refracting  than  the  internal  part. 

c.  THE  OPTOMETER  OF  YOUNG  enables  us  to  measure  spherical 
aberration  directly.  In  the  horizontal  rule  (fig.  67),  on  the  left, 
are  two  slits,  very  narrow  and  very  close.  We  look  at  the  line 


124  PHYSIOLOGIC  OPTICS 

through  these  slits  and  determine  the  central  refraction  by  ob- 
serving the  intersection  of  the  two  apparent  lines,  as  I  have  ex- 
plained in  chapter  V.  Care  must  be  taken  to  place  the  slits  so 
that  both  the  lines  appear  of  the  same  distinctness,  which  takes 
place  when  the  slits  are  almost  at  the  middle  of  the  pupil.  This 
done,  we  bring  the  quadrangular  aperture  in  front  of  the  lens, 
and  gradually  lower  the  vertical  rule  which  has  the  triangular 
plate,  so  as  to  exclude  a  continually  increasing  part  of  the  middle 
of  pupil.  We  then  see  two  intersecting  lines  which  separate  more 
and  more,  until  one  of  them  disappears  at  the  moment  when  the 
width  of  the  plate  is  equal  to  the  diameter  of  the  pupil.  We  then 
raise  the  rule  a  little,  so  as  to  again  see  two  lines,  and  measure 
the  refraction.  The  difference  between  this  measurement  and 
that  made  with  the  two  slits  placed  at  the  center  indicates  the 
degree  of  aberration. 

Young  made  two  measurements  at  once  by  using  four  slits 
of  the  horizontal  rule.  The  experiment  thus  performed  is  much 
more  elegant  and  sure,  but  it  is  often  difficult  to  succeed,  es- 
pecially if  the  pupil  is  not  dilated.  It  is  easier  to  succeed  if  the 
slits  are  brought  together  in  pairs,  leaving  a  central  interval  a 
little  greater  than  that  between  the  pairs. — With  the  four  slits 
we  see  four  lines  (fig.  68,  I)  ;  if  there  is  spherical  aberration  the 
two  central  lines  intersect  farther  away  (at  b)  than  the  peripheral 
lines  (a).  Very  frequently  the  lines  partly  blend,  so  as  to  give 
the  appearance  shown  in  figure  68,  II.  Figure  68,  III,  shows  the 
appearance  which  the  line  assumes  to  an  unsymmetrical  eye 
(left),  the  external  part  of  the  pupil  being  more  refracting  than 
the  internal. 

We  can  also  measure  with  the  two  slits  the  refraction  at  the 
middle  of  the  pupil,  as  we  did  just  before,  and  then  displace  the 
slits  successively  towards  either  border  until  one  of  the  lines 
begins  to  disappear.  We  thus  determine  the  refraction  near  the 
two  borders.  This  experiment,  by  which  we  determine  the  posi- 
tion of  the  point  c,  figure  68,  I,  is  analogous  to  that  described 


SPHERICAL  ABERRATION  125 

on  page  118,  in  which  we  covered  the  two  apertures  situated  on 
the  same  side  of  the  lens  to  measure  the  refraction  on  the  other 
side.  The  measurements  made  with  the  slits  placed  peripherally 
generally  differ  more  from  those  obtained  with  the  central  slits 
than  do  the  measurements  made  with  the  triangular  plate,  which 
is  so  also  in  the  case  of  the  lens. 

SKIASCOPIC  EXAMINATION. — While  the  methods  which  we 
have  just  mentioned  are  quite  delicate,  skiascopy  furnishes  us 
with  a  convenient  means  of  examining  the  aberration  of  the 
human  eye.  For  this  purpose  it  is  necessary  to  use  skiascopy 
with  a  luminous  point,  a  method  which  has  been  with  good  cause 
recommended  by  Jackson,  and  which  is  nothing  more  than  an 
application  of  the  principle  of  Foucault.  We  observe  the  pupil, 
while  we  form  a  distinct  image  of  a  luminous  point  on  the 
retina.  We  surround  a  flame  with  an  opaque  tube  pierced  with 
an  opening  of  one  centimeter  diameter;  it  is  the  image  of  this 
opening  that  we  project  on  the  retina  with  an  ophthalmoscope, 
and  care  must  be  taken  in  selecting  the  mirror  so  that  this  image 
may  be  distinct;  in  other  words,  so  that  the  image  of  the  open- 
ing formed  by  the  mirror  is  near  the  place  for  which  the  observed 
eye  is  focused.  If  the  observed  person  is  emmetropic,  we  place 
the  light  at  50  centimeters  or  one  meter  behind  him,  and  examine 
with  a  plane  mirror.  If  he  is  myopic,  we  use,  on  the  contrary, 
a  concave  mirror  which  projects  the  image  of  the  luminous  point 
near  his  far  point.  In  all  cases  it  is  advisable  that  the  opening 
of  the  mirror  be  quite  small,  about  2  mm.  The  pupil  of  the  ob- 
served person  must  be  dilated. 

To  examine  the  aberration,  we  make  the  observed  person 
emmetropic,  and,  placing  ourselves  at  50  centimeters  distance, 
we  project  a  light  on  the  eye.  Generally  we  will  see  at  once  the 
phenomena  of  aberration :  the  borders  of  the  pupil  are  luminous, 
separated  from  the  central  light  by  a  dark  zone.  We  approach 
until  the  ring  disappears;  if  this  takes  place  at  25  centimeters 
from  the  observed  person,  the  aberration  is  positive  and  4  D. 
If  we  do  not  perceive  the  ring,  we  move  back  as  far  as  one  meter ; 


126  PHYSIOLOGIC  OPTICS 

if  it  does  not  yet  appear,  we  try  whether  the  aberration  is  over- 
corrected  :  we  make  the  observed  person  myopic  3  D. ;  if  the  ring 
appears,  we  increase  the  myopia  until  it  disappears.  If  it  dis- 
appears with  myopia  of  4  D.,  the  aberration  is — 2  D.,  since  we 
must  take  off  2  D.,  the  observer  being  at  50  centimeters.  Brud- 
sewski,  who  determined  the  aberration  of  a  certain  number  of 
persons  in  this  way,  said  that  it  is  rare  not  to  meet  with  positive 
aberration  in  some  part  of  the  pupil.  It  happens,  indeed,  quite 
often  that  the  ring  is  incomplete,  or  even  that  there  remains 
only  a  very  small  section  of  it.  Negative  aberration  is  met  with 
most  frequently  inwards  or  upwards  in  the  pupil  where  the 
corneal  flattening  begins  soonest. 

RESULTS. — Examined  with  the  aberroscope  most  people  indi- 
cate a  certain  degree  of  aberration,  which  corresponds  closely 
to  the  nearly  spherical  (toric)  form  of  the  optic  part  of  the 


I  II 

Fig.  C9. — Deformity  of  the  shadows  in  an  eye  with  strong  spherical  aber- 
ration (Antonelli).  I,  in  a  state  of  repose;  II,  during  accommoda- 
tion. In  the  latter  case  the  aberration  is  nearly  corrected. 

cornea  (fig.  69). — Since  the  peripheral  parts  of  a  spherical 
surface  are  too  refracting,  we  can  correct  the  defect  by  flattening 
it  towards  the  periphery.  We  also  sometimes  find  people  whose 
aberration  is  corrected,  or  even  over-corrected,  towards  the 
borders,  where  the  basilar  part  of  the  cornea  comes  into  play 
(fig.  70).  And,  if  the  pupil  is  placed  a  little  eccentrically,  we 
may  thus  find  aberration  in  one  direction  and  over-corrected 


SPHERICAL  ABERRATION 


127 


aberration  in  another  (fig.  71).  Thus  the  middle  of  my  pupil  is 
slightly  myopic  and  the  upper  part  slightly  hypermetropic,  while 
the  lower  marginal  part  measures  a  myopia  of  three  dioptrics, 
which  may  even  reach  four  dioptrics  when  the  pupil  is  dilated. 
I  have,  therefore,  spherical  aberration  below  (and  on  both  sides), 
over-corrected  aberration  above. — One  of  my  friends,  who  is  an 
astronomer,  has  aberration  in  the  vertical  meridian,  while  the 
horizontal  meridian  is  corrected. 

Some  are  met  with  who  have  slightly  over-corrected  aberration 
in  the  entire  pupillary  space    (fig.   72).     These   are   probably 


Fig.  70. — Aberration 

over- corrected   towards 

the   borders. 


Fig.  71. — Aberraton 
over- corrected  above 


Fig.  72— Aberra- 

over-corrected 

everywhere. 


persons  in  whom  the  spherical  part  of  the  cornea  is  of  little 
extent. — The  ophthalmometric  measurements  of  Brudzewski, 
which  I  have  mentioned,  page  72,  enable  us  to  calculate  directly 
the  degree  of  the  aberration  of  the  cornea.  They  show  that  there 
exist,  in  this  regard,  considerable  variations.  Corneal  aberration 
is,  as  a  rule,  positive,  negative  aberration  being  rather  an  ex- 
ception. Positive  aberration  is  especially  pronounced  in  cases 
of  corneas  of  great  curvature  which  is  not  surprising,  since  the 
aberration  increases  in  very  close  proportion  to  the  central  re- 
fraction. Negative  aberration  is  met  with  most  frequently  on 
the  inner  side,  sometimes  above  or  below,  very  rarely  outside. 


128  PHYSIOLOGIC  OPTICS 

The  greatest  degree  of  aberration  which  Brudzewski  found  was 
-f-  4.5  (temporal  side),  the  least  — 2.2  D.  (nasal  side).  Gen- 
erally it  varied  between  -f-3  an^  — 1-5-  The  numbers  are  cal- 
culated for  a  distance  of  4  mm.,  starting  from  the  axis;  they 
correspond,  therefore,  to  a  maximum  dilation  of  the  pupil;  the 
values  diminish  as  we  approach  the  axis. 

Stadfeldt  measured  the  aberration  of  the  dead  crystalline  lens 
by  the  method  of  Foucault.    When  the  crystalline  lens  was  taken 

B  from  the  eye,  in  its  capsule 

and  with  the  zonula,  he 
fixed  it  in  a  cork  ring 
V  which  he  then  placed  in  a 
small  tube  filled  with  serum 
and  closed  in  front  and  be- 
hind by  plane  parallel 
plates  of  glass.  He  placed 
this  tube  on  the  support  A 
(fig.  720),  which  moved 
along  the  graduated  rule 
E  D.  The  lens  C  concen- 

Fig.  72a— Stadfeldt 's  instrument  for  meas-  trated  the  light  of  a  flame 
uring  the  aberration  of  the  crystalline  on  a  very  fine  opening 
lens  (dead).  pierced  in  the  screen  B  D. 

The  crystalline  lens  was  observed  with  a  telescope,  placed  at 
some  distance  in  the  direction  K ;  an  ocular  micrometer  permitted 
the  measurement  of  the  diameter  of  the  aberration  ring,  cor- 
responding to  a  given  distance  between  A  and  the  plate  B  D. — 
The  determination  of  the  focal  distance  of  the  central  part  is 
less  exact  by  this  method.  To  have  a  more  exact  measurement, 
Stadfeldt  removed  the  plate  B  D,  and  placed  a  microscope  of 
slight  magnifying  power  in  the  tube  K.  He  then  sighted  towards 
an  object  placed  at  a  great  distance.  By  displacing  the  cursor 
A,  leaving  the  microscope  motionless,  he  put  the  latter  in  focus, 
first  for  the  image  of  the  distant  object  formed  by  the  crystal- 
line lens,  and  then  for  the  posterior  surface  of  the  crystalline 
lens  itself.  The  difference  between  the  two  positions  of  the 


SPHEBICAL  ABERRATION  129 

cursor  A   enabled  him   to  calculate  the  focal   distance   of  the 
crystalline  lens. 

By  these  methods  Stadfeldt  proved  that  a  central  part  of  the 
crystalline  lens  (up  to  a  distance  of  2  mm.  from  the  axis)  may 
be  considered  as  aplanatic.  This  part  is  surrounded  with  a  zone 
(up  to  3.5  mm.  from  the  axis)  ;  the  aberration  of  which  is  over- 
corrected  (about  2  D.).  Very  close  to  the  borders  the  aberra- 
tion changes  sign  and  becomes  positive.  The  over-correction  is 
due  to  the  diminution  of  the  index  towards  the  periphery,  but 
very  close  to  the  borders  the  increase  of  curvature  of  the  surface 
is  so  great  that  the  diminution  of  the  index  is  not  sufficient  to 
correct  the  aberration. 

Although  aberration  may  sometimes  be  very  pronounced,  it 
does  not  seem  to  hurt  the  visual  acuity  much  as  long  as  it  con- 
tinues entirely  regular,  a  remark  which  Graefe  made  on  the  oc- 
casion of  his  celebrated  case  of  aniridia.  The  reason  is  that 
patients  do  not  use  the  part  of  the  cone  of  which  the  diameter 
is  smallest,  but  another  part  near  B,  figure  61.  Placing  a  screen 
at  this  place,  the  image  of  a  point  is  presented  as  a  point  sur- 
rounded with  a  slightly  luminous  halo;  if  the  brightness  of  the 
object  is  feeble,  as  is  most  frequently  the  case  in  the  ordinary 
circumstances  of  life,  this  halo  is  too  slight  to  be  perceived,  and 
the  image  becomes  quite  good. — We  see  (fig.  61)  that  a  section 
of  the  caustic  (the  most  luminous  part  of  the  cone)  has  the 
form  of  the  head  of  an  arrow.  The  point  of  the  arrow  is  di- 
rected backwards  in  eyes  with  ordinary  aberration  and  forwards 
in  those  with  over-corrected  aberration;  it  corresponds  to  the 
focus  of  the  central  rays,  and  it  is  this  point  which  serves  for 
vision;  but,  as  it  is  very  pointed,  it  follows  that  the  determina- 
tion of  the  refraction  cannot  be  of  very  great  exactness.  The 
spherical  aberration  acts,  in  this  regard,  as  a  narrow  diaphragm. 
If  a  lens  is  diaphragmed  much  it  becomes  very  difficult  to  deter- 
mine its  focus  exactly. — Thanks  to  this  form  of  the  caustic, 
very  regular  eyes  can  have  a  very  beautiful  visual  acuity  despite 
a  strong  aberration ;  but,  in  most  eyes,  the  refraction  is  irregular, 
so  that  patients  have  not  this  advantage  (see  chapter  X;).  I 


130  PHYSIOLOGIC  OPTICS 

think,  however,  that  they  generally  select  the  place  where  the 
section  of  the  caustic  is  smallest,  and  not  that  where  the  cone 
has  the  least  diameter. 


Bibliography. — (Euvres  de  Th.  Young,  p.  153. — Volkmann  (A.  W.)  in 
Wagner.  Handworterbuch  der  Physiologie,  Art.  Setien,  p.  292. — Meyer 
(H.).  TJeber  die  spharischen  Abweichungen  des  menschlichen  Auges. 
Poggendorfs  Ann.  LXXXIX,  p.  540. — Tscherning  (M.).  Die  monochro- 
matischen  Abweichungen  des  menschlichen  Auges.  Zeitschr.  f.  Physiol.  der 
Sinnesorgane,  VI,  p.  456. — Stadfeldt  (A.)  and  Tscherning  (M.).  Une 
nouvelle  methode  pour  etudier  la  refraction  cristallinienne,  Arch,  de 
physiol.,  July,  1896. — Jackson.  Skiascopy.  Philadelphia,  1896. — Stadfeldt 
(A.).  Eecherches  sur  I'indice  total  du  cristallin  humain.  Journal  de 
Physiologie,  November,  1899. — Brudzewski  (K.).  Beitrag  zur  Vioptrik 
des  Auges.  Archiv.  ur  Augenheilkunde,  XL,  3. 


CHAPTER  VIII 
CHROMATIC  ABERRATION 

54.  Optic  Principles. — By  receiving  on  a  screen  a  pencil  of 
white  rays  which,  after  having  passed  through  a  slit,  has  tra- 
versed a  prism,  we  obtain  what  is  called  a  spectrum,  a  luminous 
band  containing  the  entire  gamut  of  the  colors  of  the  rainbow, 
arranged  in  the  following  order :  red,  orange,  yellow,  green,  blue, 
violet.  Each  white  ray  is  divided  into  colored  rays  which  are 
refracted  differently,  the  red  the  least,  the  violet  the  most,  which 
we  express  by  saying  that  the  index  of  refraction  of  the  glass 
is  greater  for  the  violet.  If  we  speak  of  the  index  of  a  medium, 
without  more  particular  specification,  it  is  generally  the  index 
of  the  yellow  rays  (the  sodium  line)  that  is  meant. — The  dif- 
ference between  the  index  of  the  violet  and  that  of  the  red  is 
called  the  dispersion  of  the  medium.  Instead  of  receiving  the 
spectrum  on  a  screen,  we  can  observe  it  directly  by  looking  at 
the  slit  through  the  prism.  For  this  observation  the  prism  is, 
frequently  combined  with  an  astronomical  telescope  (spectro- 
scope). 

In  order  that  the  spectrum  may  be  really  pure  we  must:  i° 
make  use  of  a  very  narrow  slit ;  2°  interpose  a  lens  so  that  the 
rays  of  each  color  may  be  reunited  on  the  screen  in  a  distinct 
image  of  the  slit.  The  spectrum  is,  therefore,  in  reality  composed 
of  a  whole  series  of  images  of  the  slit;  if  these  images  are  not 
distinct  they  are  partly  overlapped  and  the  colors  are  not  pure. 
— To  obtain  a  very  great  purity  of  colors,  special  precautions 
must  be  used:  we  project  the  spectrum  on  a  screen  pierced  by 
a  slit  at  the  place  where  the  color  we  desire  to  examine  is 
formed.  Through  this  slit  an  eye  situated  behind  the  screen  re- 
ceives the  light  of  this  color,  mixed  with  a  little  white  light, 
due  to  diffusion  in  the  substance  of  the  prism  and  lens.  To 
eliminate  this  white  light,  we  observe  the  slit  through  a  second 

131 


132 


PHYSIOLOGIC  OPTICS 


prism.  It  forms  a  spectrum  which  is  very  weak  everywhere, 
except  at  the  location  of  the  color  we  desire  to  examine  (H elm- 
holt  z). — The  length  of  the  spectrum  depends  on  the  size  of  the 
angle  of  the  prism  and  on  the  degree  of  dispersion  of  the  glass : 
a  prism  of  flint  glass  produces  a  spectrum  much  longer  than  a 
prism  of  crown  glass. — Beyond  the  red  there  are  ultra-red  rays, 
which  are  invisible,  but  which  have  a  greater  caloric  effect  than 
the  visible  rays.  Beyond  the  violet  rays  there  are  likewise  ultra- 
violet rays>  which,  in  ordinary  circumstances,  are  invisible,  but 
which  act  on  photographic  plates.  They  can  be  made  visible  by 
overlaying  the  screen  with  a  "fluorescent"  liquid  (sulphate  of 
quinine,  fluorescence,  etc.).  Struck  by  the  ultra-violet  rays, 
these  substances  send  back  visible  rays,  generally  bluish  or 
greenish. — With  certain  precautions  we  can  see  directly  a  part 
of  the  ultra-violet  rays,  perhaps  because  the  retina  itself  is 
fluorescent.  Thus  Mascart  mentions  a  physicist  who  could  dis- 
tinguish the  lines  of  Fraunhofer  in  the  ultra-violet  part  of  the 
spectrum  as  far  as  the  photographic  plate  could  reproduce  them. 
We  cannot  make  the  ultra-red  rays  visible  because  they  do  not 
pass  through  the  media  of  the  eye  (Bruecke). 


Fig.  73. — Achromatic  prism. 


Fig.  74. — Prism  a  vision  directe. 


Generally,  the  media  which  have  a  greater  index  have  also  a 
greater   dispersion,    (i)    but  the  index   and  dispersion   are  not 


(1)  This  assertion  is  true  for  the  glasses  which  we  generally  use,  but  not  for 
the  new  glasses  manufactured  by  A&&e  &  Schott  at  Jena  since  1886.  They  suc- 
ceeded in  making  one  part  of  crown  glass  (with  baryta  basis)  which  has  scarcely 
any  more  dispersion  than  the  ordinary  crown  glass,  but  the  average  index  of 
which  is  equal  to  that  of  very  dense  flint,  and  another  part,  of  crown  glass,  with 
low  index  and  relatively  high  dispersion.  The  new  glasses  are  imported  for  the 
manufacture  of  microscopic  objectives  (apochromatic  systems,  see  the  following 
page)  and  also  for  photographic  objectives.  Under  the  name  of  isometropic 
glasses,  they  have  been  used  for  spectacle-making  purposes,  but,  in  this  respect, 
they  present  no  advantage. 


CH RO MAT 1C  ABERRATION  133 

proportional.  Thus  flint  glass,  for  example,  gives  a  dispersion 
nearly  double  that  of  crown  glass,  while  its  index  is  1.7  and  that 
of  crown  1.5. — If  we  combine  a  prism  of  crown  glass  with  an- 
other of  flint  glass  in  an  inverse  manner,  the  angle  of  which  is 
nearly  a  half  less,  the  dispersion  may  be  neutralized,  while  there 
remains  a  quite  considerable  part  of  the  refraction  of  the  crown 
glass.  Such  a  combination  constitutes  an  achromatic  prism 
(fig-  73). 

We  can  also  construct  combinations  of  prisms  which  give  no 
deviation  to  the  emerging  ray,  but  which  have  a  quite  consider- 
able dispersion :  we  call  these  combinations  prisms  a  vision  directe 
(fig.  74)  ;  they  are  much  used  for  the  construction  of  spectro- 
scopes. 

By  passing  through  a  lens  the  colored  rays  are  also  separated. 
As  the  index  is  stronger  for  the  blue  rays  (violet),  the  blue 
focus  is  nearer  the  lens  than  the  red  focus.  This  is  the  reason 
why  the  circle  of  diffusion  of  a  convex  lens  is  bordered  with  red 
inside  the  focus  and  with  blue  beyond. — Lenses  may  be  made 
achromatic  by  the  same  system  as  prisms:  a  convex  lens  of 
crown  glass  is  combined  with  a  concave  lens,  half  as  strong,  of 
flint.  The  circles  of  diffusion  of  such  a  lens  no  longer  present 
red  and  blue  borders,  but  there  still  remains  traces  of  other  colors 
(green  and  purple).  Zeiss  at  Jena  caused  these  latter  to  dis- 
appear also  by  combining  several  glasses  of  different  kinds, 
specially  manufactured  for  this  purpose  (apochromatic  systems). 

55.  Chromatic  Aberration  of  the  Eye. — The  eye  is  not  achro- 
matic as  was  for  a  long  time  believed.  The  question  has  played 
quite  a  curious  part  in  the  history  of  optics.  Newton  thought 
that  the  dispersion  of  a  medium  was  proportional  to  its  index 
and  that,  consequently,  the  construction  of  an  achromatic  ob- 
jective was  a  chimera;  this  is  why,  forsaking  astronomical  tele- 
scopes, he  adopted  catoptric  telescopes.  But  Euler  concluded 
that,  the  eye  being  achromatic,  it  must  be  possible  to  construct 
achromatic  lenses,  and  this  remark  led  Dolland,  the  optician, 


134  PHYSIOLOGIC  OPTICS 

to  construct  objectives  thus  corrected.  Later  Wollaston  demon- 
strated that  the  eye  is  not  achromatic.  This  is  not  the  only  time 
that  useful  results  have  been  arrived  at  by  starting  from  a  false 
hypothesis. 

56.  Experiment  of  Wollaston. — A  luminous  point  seen  through 
a  prism  gives  a  linear  spectrum.  But,  making  the  experiment, 
we  observe  that  we  cannot  see  distinctly  at  once  the  entire  extent 
of  the  spectrum.  If  the  luminous  point  is  at  a  great  distance, 
the  emmetropic  eye  sees  the  red  extremity  of  the  spectrum  as  a 
distinct  line,  while  the  blue  extremity  is  enlarged  and  frequently 
divided  into  two  ("like  the  tail  of  a  swallow").  If  we  go  nearer, 
taking  care  not  to  use  our  accommodation,  we  find  a  distance 
at  which  we  are  focused  for  the  blue  extremity,  while  the  red 
extremity  is,  in  turn,  diffuse.  The  observer  can,  therefore,  de- 
termine his  far  point  for  each  extremity  of  the  spectrum;  the 
difference  gives  the  degree  of  chromatic  aberration. 

Wollaston  has  likewise  directed  attention  to  another  phenome- 
non of  chromatic  aberration :  the  colored  borders  which  are  seen 
along  the  lines  of  the  optometer  of  Young. 

EXPERIMENTS  WITH  THE  COBALT  GLASS. — Placing  a  luminous 
point,  such  as  an  opening  in  an  opaque  screen,  inside  the  near 
point,  we  see  a  circle  of  diffusion  bordered  with  red  exactly  as 
when  we  made  the  analogous  experiment  with  the  lens ;  it  is 
more  difficult  to  see  the  blue  border  which  surrounds  the  point, 
when  it  is  situated  beyond  the  far  point.  The  experiment  is 
much  more  striking  when  the  point  is  observed  through  a  cobalt 
glass.  These  glasses  allow  only  the  blue  and  red  rays  to  pass; 
looking  at  a  luminous  point  situated  inside  the  near  point,  through 
such  a  glass,  we  see  it  blue  and  surrounded  by  a  red  halo.  If 
the  luminous  point  is  situated  beyond  the  far  point,  we  see,  on 
the  contrary,  a  red  point  surrounded  with  blue. 

EXPERIMENTS  OF  FRAUNHOFER. — This  scientist  determined  the 
distance  at  which  he  could  see  distinctly  a  spider  thread  placed 
sometimes  in  the  red  light,  sometimes  in  the  blue  light  of  the 
spectrum.  We  thus  obtain  very  exact  results. 


CHBOMATIC  ABERRATION  135 

57.  Besults. — Young  estimated  the  chromatic  aberration  of 
the  eye  at  1.3  D.,  Fraunhofer  found  1.5  to  3  D.,  Helmholtz  gives 
1.8  D.  The  number  is  difficult  to  determine  exactly,  since  the 
lowest  limit  of  the  visible  spectrum  is  not  well  defined. — The 
dispersion  of  the  eye  is  a  little  greater  than  it  would  be  if  the 
eye  were  filled  with  water. 

The  eye,  therefore,  is  not  achromatic,  and,  as  we  have  seen, 
it  is  easy  to  convince  oneself  of  it  when  the  object  is  situated 
beyond  the  far  point  or  within*  the  near  point.  But  when  the 
object  is  at  such  a  distance  that  it  can  be  seen  distinctly,  we  do 
not  see  colored  borders.  The  explanation  which  is  given  of  this 


Violet 


Fig.  75. — Chromatic  aberration  of  the  eye. 

fact  is  the  following:  Let  A  (fig.  75)  be  a  luminous  point 
which  sends  the  cone  AiBC  into  the  eye.  After  refraction  the 
white  rays  are  divided  into  colored  rays;  the  red  rays  form 
the  cone  BrC,  the  violet  rays,  which  are  more  refracted, 
the  cone  Bz>C,  and  the  eye  accommodates  itself  in  such  a  way 
that  the  retina  is  between  the  two  foci,  placed  so  that  the  red 
diffusion  circle  covers  the  blue  one  (see  fig.  75).  The  inter- 
mediary rays  of  the  spectrum,  the  yellow  and  the  green,  which 
are  the  most  luminous,  are  then  concentrated  at  the  middle 
of  the  diffusion  circle,  where  they  coincide  with  a  part  of  the 
red  and  a  part  of  the  violet,  while  the  peripheral  parts  of  the 
red  and  violet  form  a  purple  border  all  around;  but  this  border 
is  very  narrow,  and,  as  it  is  formed  by  the  extreme  rays  of  the 


136  PHYSIOLOGIC  OPTICS 

spectrum,  which  are  very  slightly  luminous,  it  is  too  weak  to  be 
perceived. — When  observing  a  luminous  point  with  an  astronom- 
ical telescope,  the  objective  of  which  is  not  very  well  achro- 
matized, the  same  phenomena  are  seen :  if  the  telescope  is  focused 
for  a  nearer  point,  the  circle  appears  surrounded  with  blue;  in 
the  contrary  case  it  is  bordered  with  red,  and,  when  the  point  is 
seen  distinctly,  it  is  surrounded  by  a  very  narrow  purple  border. 
— The  same  thing  occurs  if  the  point  A  be  replaced  by  a  white 
object :  in  the  latter  case  we  do  not  see  colored  borders. 

58.  Phenomena  of  Dispersion,  the  Pupil  Being  Partly  Covered. 
— It  is  different  if  a  part  of  the  pupil  be  covered  by  a  screen. 
Let  us  fix,  for  example,  the  sash  bar  of  a  window  through  which 
we  see  the  sky.  Covering  the  right  half  of  the  pupil  with  a 
screen,  we  see  the  border  aa  (fig.  76)  become  colored  blue,  the 
border  bb  yellow.  In  order  to  explain  this  fact  let  us  examine 
the  point  a,  the  last  luminous  point  of  the  window  on  the  right, 
and  suppose  that  the  point  A  in  figure  75  is  this 
point:  by  covering  the  half  (BO,  fig.  75)  of  the 
pupil,  instead  of  a  circle  of  diffusion  uniformly 
illuminated  by  violet  and  red,  we  have  a  circle 
the  right  half  of  which  is  violet  and  the  left  half 
red.  This  latter  half  is  covered  by  the  circle  of 
diffusion  of  the  following  point  of  the  window 
on  the  right,  and  is  not  visible;  there  remains, 
therefore,  a  blue  border  (violet)  along  the  sash  FlS-  76- 

bar.  Of  the  point  b  it  is,  on  the  contrary,  the  red  half  (yellow) 
of  the  circle  of  diffusion  which  is  not  covered. — We  frequently 
observe  very  striking  phenomena  due  to  the  chromatic  aberration 
of  the  eye,  by  fixing  black  objects  on  a  white  ground,  placed  at 
a  distance  for  which  the  eye  cannot  accommodate  itself.  Looked 
at  towards  the  sky,  the  slits  of  the  optometer  of  Young  present 
thus  very  vivid  colorings. — The  chromatic  aberration  increases 
with  the  diameter  of  the  pupil.  To  study  it,  it  is  useful,  there- 
fore, to  make  use  of  mydriatics. 


CHROMATIC  ABE  EE  AT  ION  137 

59.  Correction  of  the  Chromatic  Aberration. — We  could  correct 
the  chromatic  aberration  of  the  eye  with  a  concave  lens  of  flint, 
exactly  as  we  can  correct  the  chromatic  aberration  of  a  convex 
lens  of  crown  glass.  The  dispersion  of  flint  glass  is  about  three 
times  that  of  the  eye.  As  the  refracting  system  of  the  eye  is 
about  sixty  dioptrics,  a  concave  flint  lens  of  about  twenty 
dioptrics  would  be  necessary  to  correct  this  aberration.  A  myope 
of  twenty  dioptrics,  who  would  correct  his  ametropia  with  a 
flint  lens,  would  have,  therefore,  at  the  same  time  corrected  his 
chromatic  aberration.  An  emmetrope  would  be  obliged  to  add 
to  this  lens  a  convex  achromatic  lens  of  twenty  dioptrics  to  re- 
main emmetropic.  The  attempts  which  have  been  made  in  this 
direction  (Helmholtz,  Javal)  have  not  given  a  very  marked  im- 
provement of  the  visual  acuity. 

Bibliography. — (Euvres  de  Young,  p.  154. — Wollaston,  Phil,  trans.,  180i, 
p..  50.— Fraunhofer  (J.)  Gilberts  Ann.,  LVI,  p.  304.— v.  Bezold  (W.). 
Graefes  Arch.  f.  Ophth.,  XIV  2,  p.  1. 


CHAPTER   IX 

REGULAR  ASTIGMATISM 

60.  Optic  Principles.  Astigmatism  Produced  by  the  Form  of 
the  Surfaces. — To  account  for  the  form  of  the  astigmatic  pencil, 
the  following  experient  may  be  made.  We  combine  a  convex 
cylinder,  with  its  axis  horizontal,  with  a  convex  spherical  lens; 
the  combination  of  -[-3  cyl.  with  +6  sph.  answers  very  well. 


Ooi 


0  O 


Fig.  77. — Circles  of  diffusion  and  focal  lines  of  a  regularly  astigmatic 
system;.  After  Fuchs.  (In  order  that  the  figure  may  agree  with 
the  text,  we  must  suppose  the  first  focal  line  a  horizontal,  the  second 
"b  vertical.) 

The  pencil,  which  emanates  from  a  distant  luminous  point  and 
is  refracted  by  the  sphero-cylindrical  combination,  is  received  on 
a  screen  which  is  gradually  moved  away  from  the  lens.  Then, 
instead  of  a  circle  of  diffusion,  the  diameter  of  which  diminishes 
according  as  the  screen  is  removed  in  order  to  become  a  point 
when  the  screen  is  at  focus,  and  to  again  become  circular  be- 
yond, we  obtain  the  forms  illustrated  on  figure  77. 

The  two  straight  lines  are  called  focal  lines;  the  distance  which 
separates  them  is  called  interfaced  distance,  and  the  meridians  of 
the  optic  system  to  which  they  correspond  are  the  principal 
meridians.  Together  the  rays  no  longer  form  a  cone  in  which 
all  the  rays  pass  through  a  point,  but  a  more  complicated  system, 
characterized  by  this  peculiarity,  that  all  the  rays  pass  through 
two  short  straight  lines  perpendicular  to  each  other  (the  focal 
lines).  The  system  is  known  as  the  conoid  of  Sturm. 

The  first  focal  line  is  at  the  focus  of  the  meridian  of  greatest 
refraction  (in  our  case,  the  vertical  meridian)  ;  it  is  parallel  to 

138 


REGULAR  ASTIGMATISM 


139 


the  meridian  of  least  refraction;  the  second  focal  line  is  at  the 
focus  of  the  meridian  of  least  refraction  and  parallel  to  the 
meridian  of  greatest  refraction.  The  diffusion  spots  are  every- 
where elliptical,  except  at  one  point  of  the  interfocal  distance 
where  the  luminous  spot  is  circular. 

In  the  principal  meridians,  refraction  takes  place  as  if  the 
lenses  were  spherical;  an  incident  ray  parallel  to  the  axis  cuts 
the  latter  at  the  focus  of  the  meridian.  The  rays  which  are  not 
situated  in  the  principal  meridians  do  not  meet  the  axis;  their 
course  will  be  indicated  later  on. 

The  length  of  the  focal  lines  is  proportional  to  the  distance  of 
these  lines  from  the  lens.  Let  F'  (fig.  78)  (i)  be  the  distance 


Fig.  78.  —  pi,  horizontal  focal  line;  pz,  vertical  focal  line. 

of  the  first  focal  line,  F"  that  of  the  second,  P  the  diameter 
of  the  lens,  p^  and  p2  the  lengths  of  the  two  focal  lines.  Then 
we  have 


p±        F"  -F' 
P    : 


F" 


F' 


-    consequently  by  dividing 


p*     F" 

The  circle  of  circular  diffusion  is  at  a,  where  the  diameters 
are  equal.     It  divides  the  interfocal  distance  into   two  parts, 


(1)  We  must  suppose  that  the  vertical  meridian  has  been  made  to  rotate 
900  around  the  axis,  so  as  to  be  able  to  draw  the  two  focal  lines  In  the  same 
plane. 


140 


PHYSIOLOGIC  OPTICS 


which  are  proportional  to  the  focal  distances.  For,  designating 
the  diameter  at  this  place  by  af  and  the  two  parts  of  the  inter- 
focal  distance  by  x  and  3;  we  have: 


x+y 


and  -f 

h 


X 


,  therefore,  by  dividing, 

£L      ILL 
&  =     F' 


All  the  other  diffusion  spots  are  ellipses,  of  which  it  is  easy 
to  calculate  the  axes.  Placing  a  screen  at  a  distance  b  from  the 
second  focal  line,  we  see  (fig.  78)  that  the  axes  c  and  d  of  the 
ellipse  are  found  by  the  equations  -£_  _  b  ~  (F"~  F/)  and  —  =  ~4r 
equations  which  give  as  the  relation  between  the  axes  : 


-(F"  —  F')       F" 
k 


F' 


Knowing  the  axes  we  can  find  the  ellipse  by  construction  (fig. 
79).    We  make  a  circle  with  half  the  long  axis  d  (fig.  78)  as 


Fig.  79.  —  Construction  of  the  elliptical  diffusion  spot. 

radius,  and  draw  therein  two  diameters,  a  horizontal  BD  and  a 
vertical  AE,  and  mark  the  points  A'  and  E'  so  that 


_£_.  BD  and  A7Er  are  then  the  two  axes  of  the  ellipse,  and  we 


11EGULAE  ASTIGMATISM  141 

can  find  any  point  whatever  G1?  of  the  ellipse,  by  letting  fall  the 
perpendicular  GH  on  the  long  axis,  and  marking  the  G1  so  that 
Gi  H       c 
GH  ™  d  ' 

We  can  use  this  construction  to  find  the  course  of  the  rays 
which  are  not  situated  in  the  principal  planes.  Suppose,  indeed, 
that  one  of  these  rays  passes  through  a  given  point  of  the  lens. 
If  the  optic  system  were  spherical  and  of  the  power  of  the 
meridian  of  least  refraction,  we  would  have  a  circle  of  diffusion 
of  diameter  BD,  in  which  it  would  be  easy  to  find  the  point  K 
through  which  the  ray  would  pass,  since  the  circle  would  be  only 
a  diminished  image  of  the  lens.  Having  determined  the  position 
of  the  point  K,  we  find  the  point  K'  through  which  the  ray  really 
passes,  by  diminishing  the  distance  of  K  from  the  long  axis  in 
the  proportion  £_. 

APPLICATION  OF  THE  PRINCIPLE  OF  FOUCAULT. — Let  us  place 
the  luminous  point  a  little  beyond  the  focus  of  our  sphero- 
cylindrical  combination.  The  focal  lines  are  then  formed  at 
quite  a  great  distance.  We  receive  the  horizontal  focal  line 
on  a  screen  which  is  then  removed  and  the  eye  put  in  its  place; 
we  will  then  see  a  vertical  luminous  band  which  passes  through 
the  lens,  while  the  parts  on  the  right  and  left  are  dark.  As  we 
have  already  seen  (page  119)  the  eye  sees  luminous  the  parts  of 
the  lens  which  send  light  to, it,  and  it  is  easy  to  see  that  it  re- 
ceives under  these  circumstances  all  the  luminous  rays  from  the 
vertical  meridian,  while  it  does  not  receive  rays  coming  from  the 
lateral  parts  which  intersect  in  other  points  of  the  horizontal 
focal  line,  to  the  right  and  left  of  the  eye.  Placing  the  eye  in 
the  vertical  focal  line  we  see  a  horizontal  band. 

61.  Defects  of  the  Image. — As  the  image  of  a  point  is  never 
exactly  a  point,  the  image  of  an  object  can  never  be  really 
distinct.  Outside  the  focal  lines,  the  outlines  are  all  more  or 
less  dull.  If  the  screen  is  at  plt  the  horizontal  lines  only  are 
distinct,  if  it  is  at  />2,  it  is  the  vertical  lines  that  are  distinct. 
The  image  is  better  at  pl  than  at  />2,  since  the  first  focal  line  is 
the  shorter. 


142  PHYSIOLOGIC  OPTICS 

With  a  cylinder  which  is  strong  compared  with  the  spherical 
glass,  the  image  becomes  so  poor  that  it  is  unrecognizable;  with 
+6  spherical  combined  with  -(-3  cylindrical  of  our  test  case,  it 
is  impossible  to  form  an  image  on  a  screen.  If,  on  the  contrary, 
we  place  this  combination  sufficiently  far  from  the  eye  that  the 
image  may  be  seen  inverted,  this  image  is  pretty  good,  because 
the  pupil  of  the  observer  forms  a  diaphragm ;  but  it  is  deformed, 
all  the  dimensions  parallel  to  the  meridian  of  greatest  refraction 
being  greatly  diminished. 

62.  Astigmatic  Surfaces. — We  have  so  far  obtained  astigmatic 
refraction  by  a  combination  of  spherical  and  cylindrical  surfaces, 
but  we  can  obtain  the  same  result  by  refraction  through  a  single 
refracting  surface. — If  the  aperture  is  very  small,  this  result  is 
obtained  with  any  surface  whatever,  (i)  For,  a  small  part  of 
any  surface  always  presents  two  principal  meridians,  perpen- 
dicular to  each  other,  one  of  maximum  and  the  other  of  minimum 
curvature.  The  incident  rays,  situated  in  these  planes,  remain 
there  after  refraction  and  go  to  meet  the  axis  after  refraction ; 
the  rays  which  are  not  situated  in  these  meridians  do  not  meet 
the  axis,  but  pass  through  two  focal  lines,  perpendicular  to  the 
axis  and  situated  in  the  principal  meridians. — Among  the  sur- 
faces for  which  this  is  true,  even  for  quite  a  large  aperture,  at 
least  approximately,  there  are  two  specially  noteworthy:  the 
ellipsoid  with  three  axes  and  the  tore. 

By  rotating  an  ellipse  around  its  long  axis,  we  obtain  an 
ellipsoid  of  .revolution.  And  if  we  suppose  that  it  undergoes 
a  flattening  in  a  direction  perpendicular  to  the  long  axis,  we 
obtain  an  elUpsoid  with  three  axes.  The  luminous  point  must 
be  on  the  long  axis. — The  two  principal  meridians  are  elliptical 
(as  is  every  other  section  of  this  surface). 

The  tore  is  the  surface  which  is  obtained  by  making  a  circle 
rotate  around  an  axis  situated  in  its  plane  (ab,  fig.  80).  By  cut- 
ting a  part  near  A,  we  would  have  an  astigmatic  surface  the 


(1)  We  must  except  the  plane,  sphere,  the  part  near  the  axes  of  the  surfaces 
of  revolution,  and  that  near  the  points  called  umbilical  of  other  surfaces,  sup- 
posing the  incidence  normal.  Otherwise,  the  refraction  is  always  astigmatic. 


EEGTJLAR  ASTIGMATISM  143 

principal  meridians  of  which  would  be  circular;  one  would  have 
the  same  radius  as  the  circle  (Rj)  ;  the  radius  of  the  other  (R2) 
would  be  equal  to  the  distance  of  the  axis  from  the  apex  of  the 
circle.  The  luminous  point  must  be  on  the  prolongation  of  AC. 
Even  with  these  surfaces  a  pure  astigmatic  action  is  not  ob- 
obtained,  when  the  aperture  is 
a  little  large.  It  is  clear  that  on 
account  of  the  spherical  aberra- 
tion the  peripheral  parts  of  the 
principal  meridians  of  the  tore 
must  have  a  greater  refraction 
than  the  central  parts;  also  the 
astigmatism  of  a  peripheral  zone 
becomes  greater  than  that  of  the 
central  part,  since  the  refraction 

increases  more  rapidly  towards 

,,  •   ,  .     ,,  <     Fig.  80. — By  the  revolution  around 

the  periphery  in  the  most  curved  .  , .   ,.        , 

the   straight  line   ab,   the   circle 

principal  meridian. — On  account  produces  a  torus, 
of  the  flattening  towards  the  periphery,  the  aberration  is  less  for 
the  ellipsoid;  one  of  the  meridians  may  even  be  aplanatic  for 
a  distant  object,  but  then  the  other  meridian  is  either  over- 
corrected  or  under-corrected,  so  that  the  astigmatic  effect  is 
never  pure. 

63.  Astigmatism  by  Incidence. — Let  us  place  a  spherical  lens 
at  some  distance  from  a  luminous  point  and  form  the  image  of 
this  point  on  a  screen;  then  make  the  lens  rotate  around  a 
vertical  axis.  The  screen  immediately  ceases  to  be  at  the  point ; 
we  must  move  it  nearer  the  lens,  and  we  find  at  the  same  time 
that  the  refracted  pencil  is  astigmatic.  The  horizontal  focal  line 
is  farther  from  the  lens  than  the  vertical  focal  line.  The  refrac- 
tion has,  therefore,  increased  in  both  meridians,  but  more  in  that 
which  contains  the  axis  of  the  lens  and  the  luminous  point. 

The  focal  lines  are  far  from  being  distinct,  especially  if  we 
do  not  use  a  small  diaphragm.  They  are  rather  diffusion  spots 
greatly  lengthened  in  one  or  other  direction. — But  the  pencil 
has  one  true  focal  line  which,  in  our  case,  is  horizontal ;  we  find 


144 


PHYSIOLOGIC  OPTICS 


it  by  making  the  screen  rotate  around  a  vertical  axis,  but  in  a 
direction  the  reverse  of  that  of  the  lens  (fig.  81). 


Fig.  81. — Focal  line  of  a  lens  placed  obliquely. 

A  pencil  reflected  or  refracted  obliquely  by  a  spherical  surface 
is  also  astigmatic  by  incidence.  It  is  the  same  phenomenon 
which  constitutes  spherical  aberration. 

Let  cabd  (fig.  82)  be  an  incident  pencil  parallel  to  the  axis 
of  a  refracting  spherical  surface.  Suppose  that  the  pencil  is 


Astigmatism  by  incidence.- 


Fig.  82. 
-F',  first  focal  line;  F"F"',  second  focal  line. 


cylindrical,  so  that  ab  is  the  diameter  of  the  small  round  spot 
which  represents  the  aperture  of  the  surface :  ab  is  then  one  of 
the  principal  meridians  and  the  diameter  perpendicular  to  ab  is 
the  other.  On  account  of  the  spherical  aberration  the  ray  aF' 
meets  the  axis  nearer  the  surface  than  the  ray  b¥'.  The  first 
focal  line,  which  is  perpendicular  to  the  plane  of  the  paper,  is  at 
F',  for,  if  we  imagine  the  entire  figure  rotating  around  the  axis, 


EEGULAR  ASTIGMATISM  145 

F'  describes  an  arc  of  a  circle,  a  small  part  of  which  may  be 
considered  as  a  straight  line,  and  it  is  easy  to  see  that  all  the 
rays  of  our  pencil  must  pass  through  this  straight  line  (at  least 
approximately).  As,  on  the  other  hand,  the  rays  must  all  meet 
the  axis,  F"  F'"  is  the  second  focal  line. — Here  again  the 
meridian  of  greatest  refraction  is  that  which  contains  the  axis. 

When  the  incidence  is  oblique,  all  the  surfaces,  the  plane  sur- 
faces included,  give  astigmatism  by  refraction. 

It  is  the  same  in  the  case  of  reflection,  but  then  the  plane 
surfaces  are  an  exception.  Ordinary  mirrors  are  not  exempt 
from  this  defect  on  account  of  the  refraction  through  the  thick- 
ness of  the  glass  which  is  in  front  of  the  coating.  The  best 
images  that  we  can  obtain  are  those  formed  by  reflection  on  a 
surface  of  mercury,  especially  when  the  layer  is  very  thin:  the 
pencil  is  not  astigmatic  at  all.  (i) 

64..  Astigmatism  of  the  Human  Eye.  Historical. — This  defect 
of  the  human  eye  was  discovered  by  Thomas  Young  in  1801. 
He  never  noticed  that  his  vision  was  defective,  and  claimed  that 
he  saw  as  well  as  most  people.  He  proved  the  defect  in  his  own 
eye  by  means  of  his  optometer,  and  also  by  observing  the  forms 
of  the  circles  of  diffusion  produced  by  a  luminous  point.  He 
measured  its  degree  by  means  of  the  optometer  and  expressed 
it,  as  we  still  do,  by  the  difference  of  refraction  of  the  two 
meridians.  He  had  1.7  D.  of  astigmatism  against  the  rule.  He 
proved  that  his  astigmatism  was  not  seated  in  the  cornea,  because, 
by  performing  his  celebrated  experiment  of  putting  the  eye  under 
water  and  substituting  a  spherical  lens  for  the  cornea  (see  page 
202),  he  found  the  same  degree. — He  attributed  the  astigmatism 
to  the  obliquity  of  the  crystalline  lens,  which  obliquity  he  thought 
much  greater  than  it  really  is,  and  remarked  that  the  defect  could 
be  corrected  with  glasses  placed  obliquely  in  front  of  the  eye. 

The  astronomer  Airy,  a  professor  at  Cambridge,  was  the  first 
who  corrected  the  defect  by  a  cylindrical  glass  (1827).  He  had 


(1)  It  is  claimed,  however,  that  we  can  still  observe  a  trace  of  astigmatism, 
in  this  case,  with  the  telescopes  of  the  greatest  magnifying  power.  This  astig- 
matism might  be  due  to  the  fact  that  the  surface  is  not  really  plane  on  account 
of  the  spherical  form  of  the  earth. 


146  PHYSIOLOGIC  OPTICS 

high  compound  myopic  astigmatism  of  the  left  eye,  which  he. 
studied  and  measured  by  means  of  a  luminous  point. — Later, 
Colonel  Goulier  likewise  studied  this  defect  and  prescribed  cylin- 
drical glasses  to  a  certain  number  of  patients. 

It  was  only  after  the  invention  of  the  ophthalmometer  by 
Helmholtz  that  the  measurements  of  Knapp  and  Bonders  drew 
attention  to  this  prevalent  anomaly  of  the  human  eye.  The 
works  of  these  two  investigators  appeared  almost  at  the  same 
time,  but  those  of  Bonders  had  greater  influence.  He  was,  in 
fact,  the  first  to  have  cylindrical  glasses  put  in  the  test  case, 
which  greatly  contributed  to  their  more  general  use.  The 
methods  used  for  the  examination  of  patients  were  quite  de- 
fective. The  luminous  point  was  especially  used  to  find  the 
meridians,  and  the  refraction  of  each  meridian  was  then  meas- 
ured by  means  of  the  stenopaic  slit  and  spherical  glasses. — A 
little  later  Javal  introduced  the  examination  by  the  star  figure 
and  cylindrical  glasses. 

65.  Physiologic  Astigmatism. — It  is  rare  to  find  an  eye  com- 
pletely free  from  astigmatism;  but  when  the  degree  is  slight,  it 
scarcely  affects  the  vision.  We  call  this  astigmatism  physiologic. 
It  is  a  disputed  question  at  what  degree  we  should  begin  to 
consider  astigmatism  pathologic;  some  have  placed  the  limit  at 
0.5  D.  or  at  0.75  D.,  others  at  I  D.  or  1.5  D,  In  certain  people 
we  can  improve  vision  with  a  cylinder  of  0.75 ;  others,  on  the 
contrary,  experience  no  improvement,  although  they  may  have 
really  the  same  degree  of  astigmatism.  The  aperture  of  the 
pupil,  and  especially  the  greater  or  less  regularity  of  the  astig- 
matic pencil,  here  play  an  important  part.  One  of  the  best  means 
of  disclosing  low  degrees  of  astigmatism  consists  in  observing 
the  form  under  which  a  luminous  point  appears  when  placed 
at  different  distances.  If  the  luminous  point  indicates  a  trace 
of  astigmatism,  we  can  generally  also  verify  it  by  the  star 
figure  and  a  weak  cylindrical  lens,  by  placing  the  latter  at  first 
in  the  correct  position  and  then  in  the  contrary  position.  The 
patient  then  tells  that  the  former  position  equalizes  the  lines 
better  than  the  latter. 


KEGULAR  ASTIGMATISM  147 

66.  Corneal  Astigmatism. — The  principal  seat  of  astigmatism 
is  in  the  anterior  surface  of  the  cornea,  which  is  not  strange, 
since  it  is  at  this  place  that  the  principal  change  of  index  occurs. 
A  deformity  of  one  of  the  internal  surfaces  of  the  eye,  which, 
at  the  anterior  surface  of  the  cornea,  would  produce  considerable 
astigmatism,  has  only  slight  effect  on  account  of  the  little  dif- 
ference of  index  of  the  media.     The  refraction  is  expressed, 
as  we  have  seen,  by  (» ~ *>  100°   (see  page  16),  that  is  to  say,  for 

R 

the  cornea,  by  ??!i5  and,  for  one  of  the  internal  surfaces,  bygl 

*  K.  .    K.  * 

The  same  deformity  would,  therefore,  produce  an  effect  five  or 
six  times  less. 

We  may  conceive  also  that,  in  the  normal  eye,  astigmatism  by 
incidence  could  scarely  play  any  part,  since  the  visual  line  passes 
approximately  through  the  center  of  curvature  of  the  cornea  and 
through  the  middle  of  the  pupil.  It  is  otherwise  in  cases  where 
there  exists  a  considerable  displacement  of  the  pupil  (corectopia), 
and  especially  in  the  case  of  an  artificial  pupil. — Under  ordinary 
circumstances,  therefore,  it  is  the  form  of  the  anterior  surface 
of  the  cornea  that  principally  determines  astigmatism;  the  ex- 
amination of  this  surface  thus  plays  an  important  part  in  the 
search  for  astigmatism. 

67.  Measurement   of   Corneal  Astigmatism. — There  exist   dif- 
ferent means  of  examining  whether  the  cornea  is  astigmatic  and 
of  estimating  the  degree  of  its  deformity  (disc  of  Placido,  kerato- 
scope  of  de  Wecker  and  Masselon,  etc.)  ;  but,  to  measure  it,  one 
can  scarcely  think  of  using  any  other  means  than  the  ophthal- 
mometer  of  Javal  and  Schioetz,  which  we  have  already  described. 
The  progress  which  it  marks,  compared  with  old  ophthalmo- 
meters,  consists  especially  in  the  facility  with  which  we  find  the 
principal   meridians   by  means   of  the   difference   in   the   level 
(denivellation) .    If  the  arc  is  in  a  principal  meridian,  the  images 
of  the  two  mires  must  be  on  the  same  level  and  the  black  lines 
which  are  at  the  middle  of  the  mires  must  be  in  the  prolongation 
of    each    other.      Outside    the    principal    meridians    there    is   a 


148 


PHYSIOLOGIC  OPTICS 


difference  in  the  level   (denivellation)  greater  in  proportion  as 
the  astigmatism  is  more  pronounced. 


Fig.  83. — Explanation  of  the  difference  in  the  level  (denivellation). 

To  explain  this  phenomenon,  let  us  examine  a  spherical  cornea 
after  having  removed  the  doubly  refracting  prism  from  the  in- 
strument which  then  acts  as  a  simple  telescope.  We  then  see 
only  the  images  of  the  two  mires.,  separated  by  an  interval  of 
about  3  millimeters.  By  rotating  the  arc  these  images  describe 
a  circle.  Let  ABCD,  figure  83,  be  this  circle  to  which  the  images 
of  the  mires  always  remain  tangents.  Let  us  replace  the  prism 
in  position.  Then  the  images  are  in  the  same  meridian  as  the 
mires  themselves,  and  as  the  doubling  (dedoublement)  of  the 
prism  takes  place  exactly  in  this  meridian  there  is  no  difference 
in  the  level, — If  we  replace  the  spherical  cornea  by  an  astigmatic 
cornea,  the  vertical  meridian  of  which  is  the  more  curved,  the 
circle  ABCD  is  replaced  by  the  ellipse  AEBF  which  is  con- 
structed as  shown  on  page  140  by  reducing  the  distance  of  each 


EEGULAE  ASTIGMATISM  149 

point  from  AB  in  the  proportion  of  the  radii  of  the  two  principal 
meridians.  By  this  construction  the  dotted  diameter  becomes 
the  diameter  KL,  on  which  the  images  now  are.  The  latter 
are,  therefore,  no  longer  situated  in  the  meridian  of  the  mires, 
and  as  the  prism  always  acts  in  the  direction  parallel  to  this 
meridian,  it  follows  that  on  obtaining  contact  the  two  images 
are  not  on  the  same  level.  Only  when  the  arc  is  in  one  of  the 
principal  meridians  the  mires  and  their  images  are  in  the  same 
plane  and  there  is  no  difference  in  the  level. 

We  can  account  for  the  difference  between  the  image  pro- 
duced by  a  spherical  cornea  and  that  of  an  astigmatic  cornea,  by 
drawing  on  a  sheet  of  paper  a  circle  with  two  oblique  diameters, 
perpendicular  to  each  other,  and  observing  the  inverted  image 
formed  by  a  strong  spherical  lens  held  at  some  distance  from 
the  eye.  The  image  is  identical  with  the  drawing;  but  if  a  con- 
vex cylinder  with  horizontal  axis  be  added,  the  circle  is  replaced 
by  an  ellipse  with  the  long  axis  horizontal,  and  the  two  diameters 
form  between  them  obtuse  angles  above  and  below. 

After  having  placed  the  ocular  in  focus  for  the  spider  thread, 
and  then  the  instrument  in  focus  for  the  eye,  we  begin  by  finding 
the  meridian  of  least  refraction.  We  place  the  mires  in  contact 
and  make  the  arc  rotate  90°.  This  done,  the  images  of  the  mires 
partly  overlap,  and  the  number  of  gradations  overlapped  indi- 
cates the  degree  of  astigmatism  in  dioptrics. — If  very  exact 
measurements  are  desired,  it  is  preferable  to  find  each  of  the 
meridians  separately,  and  to  obtain  contact  in  each  of  them.  We 
read  the  refraction  of  each  meridian  on  the  arc,  and  the  differ- 
ence indicates  the  astigmatism. — We  sometimes  observe  that  the 
two  principal  meridians  are  not  exactly  perpendicular  to  each 
other;  this  is  due  to  the  relatively  great  distance  between  the 
mires ;  for,  the  principal  meridians  of  a  minute  part  of  a  surface 
are  always  perependicular  to  each  other. — This  is  attributable  to 
the  fact  that  the  meridians,  instead  of  being  plane  sections  of 
the  cornea,  possess  a  certain  curvature. 

68.  Regular  Corneal  Astigmatism. — We  distinguish  between 
direct  astigmatism  or  astigmatism  with  the  rule,  in  which  the 


150  PHYSIOLOGIC  OPTICS 

meridian  of  greatest  refraction  does  not  differ  much  from  the 
vertical,  and  perverse  astigmatism  or  astigmatism  against  the 
rule,  in  which  the  horizontal  meridian  is  that  of  greatest  re- 
fraction. If  the  direction  of  the  meridians  differs  much  from 
the  horizontal  and  vertical  directions,  we  say  that  the  astig- 
matism is,.oblique. 

Schioetz  and  Nordenson  have  compiled  statistics  on  the  di- 
rection of  the  corneal  astigmatism  in  school  children.  Following 
are  the  results  obtained  by  Nordenson: 

Corneal  astigmatism,  none 9  per  cent. 

—  with  the  rule 77       — 

against  the  rule 1      — 

oblique   12      — 

Thirty  per  cent,  had  astigmatism  of  at  least  I  D.,  2  per  cent, 
an  astigmatism  over  1.5  D. — It  seems  that  astigmatism  against 
the  rule  becomes  more  frequent  with  age,  and  that  astigmatism 
with  the  rule  changes  into  astigmatism  against  the  rule  under  the 
influence  of  an  increase  of  tension.  Pfalz  and  G.  Martin  have 
thus  found  astigmatism  against  the  rule  very  common  in  glauco- 
matous  patients,  and  the  experimental  researches  of  Eissen  on 
rabbits'  eyes  confirm  this  result. 

Except  in  post-operative  cases,  corneal  astigmatism  only  very 
rarely  exceeds  the  degree  of  5  to  6  D.;  astigmatism  against  the 
rule  and  oblique  astigmatism  are  never  so  pronounced. — If  there 
is  a  difference  between  the  degree  of  the  astigmatism  of  the 
two  eyes  of  the  same  person,  we  generally  find  that  the  most 
astigmatic  eye  has  the  maximum  curvature  greater  and  the 
minimum  curvature  less  than  those  of  the  other  eye,  but  the 
difference  is  generally  greater  for  the  meridian  of  greatest  re- 
fraction (Javal). 

69.  Belations  Between  Ophthalmometric  and  Subjective  Astig- 
matism.— We  have  said  that  the  first  Ophthalmometric  measure- 
ments were  made  by  Donders  and  Knap  p.  They  noticed  that 
there  existed  a  certain  difference  between  the  Ophthalmometric 
and  subjective  measurements.  They  attributed  this  difference 


REGULAR  ASTIGMATISM  151 

to  an  astigmatism  of  the  crystalline  lens  which  would  act  in  a 
direction  contrary  to  that  of  the  cornea.  Since  then  much  has 
been  said  of  crystalline  astigmatism,  but  what  has  been  said 
about  it  is  purely  hypothetical,  for  if  I  except  some  measure- 
ments which  I  have  made  with  the  ophthalmophakometer,  and 
to  which  I  shall  refer  later,  I  do  not  think  that  ony  one  has  ob- 
served directly  astigmatism  of  the  crystalline  lens.  Now,  the 
difference  between  ophthalmometric  and  subjective  astigmatism 
may  be  attributed  to  many  other  causes.  To  assume  nothing  as 
to  the  nature  of  this  astigmatism  I  shall  call  it  supplementary 
astigmatism.  According  to  most  investigators  the  part  which 
it  plays  is  the  following: 

i°  If  there  is  no  ophthalmometric  astigmatism,  we  generally 
find  a  slight  subjective  astigmatism  against  the  rule; 

2°  If  the  ophthalmometric  astigmatism  is  against  the  rule,  the 
subjective  astigmatism  is  generally  against  the  rule  and  greater; 

3°  If  the  ophthalmometric  astigmatism  is  with  the  rule  and  of 
a  value  intermediate  between  I  and  3  D.,  the  subjective  astig- 
matism generally  differs  only  slightly  from  it ; 

4°  If  the  ophthalmometer  gives  an  astigmatism  with  the  rule 
and  greater  than  3  D.,  the  subjective  astigmatism  is  also  with 
the  rule,  frequently  greater. 

Javal  tried  to  express  the  relation  between  subjective  astig- 
matism (Ast)  and  opththalmometric  astigmatism  (Asc)  by  the 
empiric  formula: 

ASt  =  k  +  p.  Asc, 

in  which  formula  k  and  p  are  two  constants,  £=0.5  D.  against 
the  rule  and  p=i. 25. — This  formula  would  give  the  following 
relation : 

Against  the  rule.  ^^^^^^^   With  the  rule. 

As.  ophtTiT^T  —  0  —  1—2-  3—4—  5—6  dipotries 
As.  subj.  3  —  1.75  —  0.5  —0.75  —  2  —  3.25  —  4.5  —  5.75  —  7  dipotries 

Against  the  rule.  With  the  rule. 

It  is  well  understood  that  this  permits  of  many  exceptions, 
for  supplementary  astigmatism  depends  on  so  many  factors,  that 


152 


PHYSIOLOGIC  OPTICS 


it  is  very  difficult  to  give  a  general  expression  of   its  value. 
Among  these  factors  I  shall  state  the  following: 

i°  The  Deformity  of  the  Internal  Surfaces. — Although  these 
deformities,  as  I  have  already  remarked,  play  quite  an  im- 
portant part  in  the  literature,  this  question  has,  up  to  the  present, 
been  completely  ignored.  To  give  an  idea  of  the  part  which 
they  might  play,  I  add  the  following  table,  which  gives  the  re- 
sults for  some  eyes  I  have  measured : 

Mme  T.       Dr.  B.  M.  V. 

Thickness  of  cornea 1.15mm       i.06mm  1.31mm 

Position    of    the    anterior    surface    of    the 

crystalline    3.54mm       4.24mm  3.66mm 

Thickness  of  crystalline 4.06mm       3.98mm  4.25mm 

Anterior  surface  of  cornea: 

Eadius.     Horizontal  meridian 7.98mm      7.78mm  8.29mm 

Vertical  meridian 7.60mm       7.90mm  8.33mm 

Horizontal  refraction   47.24  D.      48.46  D.  45.48  D. 

Vertical  refraction  49.60  D.     47.72  D.  45.26  D. 

Posterior  surface  of  the  cornea: 

Eadius.     Horizontal  meridian 6.22mm       5.66mm  6.17mm 

Vertical  meridian 5.55mm       5.11mm  5.87mm 

Horizontal  refraction — 4.73  D.   — 5.19  D.   — 4.77  D. 

Vertical  refraction  — 5.30  D.   — 5.76  D.    — 5.01  D. 

Anterior  surface  of  the  crystalline  lens : 

Eadius.     Horizontal  meridian 10.20mm     12.26mm  10.42mm 

Vertical  meridian 10.10mm     10.09mm  9.33mm 

Horizontal  refraction    6.13  D.        5.10  D.  6.00  D. 

Vertical  refraction  6.19  D.        6.19  D.  6.70  D. 

Posterior  surface  of  the  crystalline  lens: 

Eadius.     Horizontal  meridian 6.17mm      6.38mm  6.73mm 

Vertical  meridian 6.24mm       7.nmm  8.49mm 

Horizontal  refraction    9.53  D.        9.22  D.  8.73  D. 

Vertical  refraction  9.42  D.        8.27  D.  6.93  D. 

Astigmatism  in  Dioptrics:    (1) 

Anterior  surface  of  the  cornea 2.36  d         0.74  i  0.22  i 

Posterior  surface  of  the  cornea 0.57  i          0.57  i  0.24  i 

Anterior  surface  of  the  crystalline  lens 0.06  d         1.09  d  0.70  d 

Posterior  surf  ace  of  the  crystalline  lens ...       0.11  i          0.95  i  1.81  i 

Complete  system  1.40  d         1.05  i  1.62  i 


(1)    [Here  d   (direct)   stands  for  astigmatism  with   the  rule  and  i    (indirect) 
for  that  against  the  rule.] — W. 


REGULAR  ASTIGMATISM  153 

Although  we  manifestly  cannot  draw  general  conclusions  from 
the  measurements  of  three  eyes,  I  wish,  however,  to  direct  at- 
tention to  some  of  these  results.  Wje  observe  in  the  first  place 
that  the  vertical  meridian  of  the  posterior  surface  of  the  cornea 
presents  a  more  pronounced  curvature  than  the  horizontal 
meridian.  This  condition  is  repeated  in  the  three  eyes  to  which 
I  here  refer,  as  well  for  the  first,  the  anterior  surface  of  which 
presents  astigmatism  with  the  rule,  as  for  the  other  two  in 
which  it  presents  astigmatism  against  the  rule.  I  have  also  met 
the  same  deformity  in  other  eyes  which  I  have  measured,  so 
much  so  that  there  is  reason  to  believe  that  the  condition  is 
general.  It  is  a  deformity  analogous  to  that  which,  in  the  case 
of  the  anterior  surface  of  the  cornea,  produces  astigmatism  with 
the  rule;  but,  as  the  posterior  surface  acts  like  a  concave  lens, 
this  deformity  produces  astigmatism  against  the  rule.  It  is 
probably  for  this  reason  that  eyes,  which  have  no  ophthalmo- 
metric  astigmatism,  generally  have  subjective  astigmatism  against 
the  rule.  The  influence  of  the  posterior  surface  of  the  cornea 
must  correspond  partly  with  the  term  k  of  the  formula  of  Javal. 

As  to  the  crystalline  surfaces,  we  observe  that  the  anterior 
surface  presents  in  the  three  cases  astigmatism  with  the  rule, 
the  posterior  surface  astigmatism  against  the  rule.  I  do  not 
know  whether  it  is  a  coincidence  or  whether  it  indicates  a  general 
rule. 

2°  The  obliquity  of  the  crystalline  lens  must,  after  what  we 
have  said  on  refraction  by  lenses  placed  obliquely  (page  143), 
produce  astigmatism  against  the  rule,  but  very  little,  at  most  a 
half  dioptry,  and  perhaps  less,  if  the  special  structure  of  the 
crystalline  lens  results  in  compensating  the  effect  of  its  obliquity 
as  certain  authors  (Hermann)  have  supposed. 

3°  Mention  has  been  made  of  an  astigmatic  accommodation 
of  the  crystalline  lens,  which  would  have  the  effect  of  correcting 
the  corneal  deformity,  and  often  even  over-correcting  it.  In  my 
opinion  this  astigmatic  accommodation  is  not  sufficiently  demon- 
strated ;  I  shall  speak  of  it  forthwith. 

4°  We  must  not  forget  the  influence  of  the  distance  of  the  cor- 
recting glass  from  the  eye,  in  consequence  of  which  the  concave 


154  PHYSIOLOGIC  OPTICS 

correcting  glass  is  stronger,  the  convex  glass  weaker  than  the 
true  astigmatism.  This  influence  makes  itself  felt  the  more 
according  as  the  glass  is  stronger,  and,  in  order  to  calculate  it, 
we  must  take  into  account  not  only  the  cylindrical  glass,  but  also 
the  spherical  glass  with  which  it  is  combined  (Ostwalt}  (i). — 
If  certain  authors  have  found  that  the  subjective  astigmatism 
with  the  rule  frequently  exceeds  that  found  with  the  ophthalmo- 
meter  (the  factor  p  of  Javal),  it  is  due,  perhaps,  to  the  fact  that 
they  generally  use  concave  cylinders. 

5°  Among  the  factors  which  play  a  part  in  supplementary 
astigmatism,  the  most  important  is  probably  the  variation  of  the 
astigmatism  in  the  different  zones  of  the  cornea.  The  peripheral 
zones  frequently  present  a  value,  and  sometimes  also  a  direction 
more  or  less  different  from  those  of  the  central  zones.  This, 
among  other  things,  follows  from  the  measurements  of  the 
peripheral  parts  of  the  cornea  made  by  Sulzer;  but  it  is  especially 
after  I  began  to  work  with  the  optometer  of  Young  that  I  fre- 
quently found  considerable  differences  between  the  refraction, 
of  different  parts  of  the  pupillary  space,  and  that  I  became  con- 
vinced of  the  importance  of  these  differences.  There  certainly 
exist  some  regularly  constructed  eyes,  in  which  the  astigmatism 
is  nearly  the  same  in  the  whole  pupillary  space,  but  most  eyes 
are  more  or  less  irregular.  Entirely  regular  astigmatism  is  only 
imaginary. — This  explains  also  the  hesitancy  of  many  patients 
when  tested  with  different  cylindrical  glasses.  We  have  all  met 
cases  in  which  it  is  almost  impossible  to  obtain  a  definite  answer 
from  the  patient.  Sometimes  he  prefers  one  cylinder,  sometimes 
another  somewhat  different,  and,  at  each  new  examination,  he 
manifests  a  different  preference.  Most  frequently  if  the  patient 
hesitates,  he  has  good  reasons  for  doing  so. — Examination  with 
the  luminous  point  (see  chap.  X:),  which  has  been  much  ne- 
glected, but  which  we  have  used  for  some  time  at  the  laboratory 
of  Sorbonne,  shows  why  the  patient  hesitates  and  why  we  fre- 
quently do  not  obtain  a  very  encouraging  result  by  correction. 


(1)    [See  also  an  article  by  the  translator  in  the  Archives  of  Ophthalmology, 
Vol.  XXII,   No.   1,   1893,  where  this  question  is  discussed  fully.] — W. 


REGULAR  ASTIGMATISM  155 

70.  Astigmatic  Accommodation. — The  question  of  astigmatic 
accommodation  has  been  much  discussed  for  some  years  past. 
It  was  Dobrowolsky  who  first  expressed  the  idea  that  astigmatic 
patients  could  partly  correct  their  defect  by  producing  a  de- 
formity of  the  crystalline  lens  in  a  contrary  direction,  by  an  ir- 
regular contraction  of  the  ciliary  muscle.  He  thus  supposed  a 
latent  astigmatism  which  could  be  made  manifest  by  instilling 
atropine,  exactly  as  in  the  case  of  hypermetropia. — Later,  the 
idea  was  adopted  by  Javal,  and  pushed  to  its  extreme  conclusions 
by  G.  Martin,  Vacher  and  others,  who  went  so  far  as  to  find  in 
this  astigmatic  accommodation  the  origin  of  a  series  of  diseases : 
blepharitis,  keratitis,  migraine  and  even,  in  certain  cases,  cataract. 
Some  time  ago  a  reaction  set  in;  most  of  the  authors  in  later 
years,  like  Eriksen,  Sulzer  and  especially  George  Bull,  do  not 
admit  astigmatic  accommodation. 

The  advocates  of  astigmatic  accommodation  based  their  belief 
especially  on  the  change  of  the  astigmatism  observed  on  instilling 
atropine.  The  phenomenon  is,  in  all  probability,  due  to  the  fact 
that  the  astigmatism  of  the  peripheral  parts  differs  from  that  of 
the  central  part;  in  ordinary  circumstances  these  parts  are  out- 
side the  pupil,  but  in  consequence  of  atropinization  the  latter 
is  dilated  so  as  to  allow  the  peripheral  parts  to  come  into  play. 
The  area  of  these  peripheral  parts  is  generally  greater  than  that 
of  the  central  art  which  corresponds  to  the  pupil  in  ordinary 
circumstances.  Suppose,  for  example,  that  the  diameter  of  the 
pupil  may  be  brought  from  4  to  8  millimeters.  The  area  of  a 
circle  being  expressed  by  r2n,  that  of  the  ordinary  pupil  is  about 
12  square  millimeters  and  that  of  the  dilated  pupil  about  50 
square  millimeters.  The  pupil  has  consequently  increased  by  38 
square  millimeters,  or  about  three  times  its  size.  Thus  much 
more  light  enters  through  these  peripheral  parts;  and  it  is  not 
surprising  that  this  fact  greatly  influences  the  answers  of  the 
patient.  All  the  observations  of  a  change  of  astigmatism  after 
instilling  atropine  prove  nothing,  therefore,  in  favor  of  astig- 
matic accommodation.  It  has  been  proposed  to  study  the  question 
by  placing  before  the  eye  a  diaphragm  of  the  size  of  the  un- 
dilated  pupil,  but  I  do  not  see  how  we  could  assure  ourselves 


156  PHYSIOLOGIC  OPTICS 

whether  the  position  of  the  diaphragm  really  corresponded  with 
that  of  the  undilated  pupil. — The  only  observations  in  favor  of 
astigmatic  accommodation  which  could  lay  claim  to  some  value, 
are  those  in  which  the  observer,  provided  with  a  weak  cylinder, 
begins  by  seeing  distinctly  one  line  of  the  star  figure  and  ends 
by  seeing  all  with  the  same  distinctness.  But  the  observations 
of  this  kind  which  have  been  published  are  by  no  means  beyond 
all  criticism.  If  any  one  desires  to  again  perform  this  experi- 
ment he  had  better  use  a  luminous  point:  after  having  placed 
a  weak  cylinder  before  the  eye,  it  would  be  necessary  to  observe 
the  different  forms  under  which  the  luminous  point  would  be 
seen  at  different  distances  (see  the  following  chapter)  and  to 
repeat  this  examination  after  having  worn  the  cylinder  for  an 
hour  or  two,  to  see  if  the  figures  had  undergone  any  change. 

The  alleged  astigmatic  accommodation  was  always  of  a  very 
low  degree,  i  D.  to  1.5  D.  at  most.  Frequently,  in  order  to  dis- 
cover it,  a  very  persistent  atropinization  was  necessary,  lasting 
as  much  as  fifteen  days  and  even  until  symptoms  of  poisoning 
appeared.  I  think  that  frequently  the  patient,  weary  of  the 
struggle,  ended  by  answering  all  that  was  desired. 

71.  Post-operative  Astigmatism. — If  we  examine  the  cornea 
eight  days  after  the  extraction  of  a  cataract,  we  find  an  enorm- 
ous astigmatism  against  the  rule,  sometimes  reaching  12  or  14  D. 
The  vertical  meridian  is  flattened,  probably  in  consequence  of 
the  interposition  of  an  exudation  between  the  Tips  of  the  wound ; 
the  phenomenon  is  more  pronounced  if  there  exists  a  hernia  of 
the  iris.  This  astigmatism  diminishes  gradually ;  it  may  dis- 
appear altogether,  but  generally  one  or  two  dioptrics  remain. 
For  this  reason  it  is  prudent  to  postpone  the  selection  of  spec- 
tacles for  two  or  three  months  after  the  extraction,  or,  if  the 
patient  desires  to  have  them  immediately,  to  warn  him  that  it 
will  be  necessary  to  change  them  after  two  months.  Contrary 
to  what  we  would  expect,  the  agreement  between  the  subjective 
astigmatism  and  the  ophthalmometric  measurement  is  less  than 
for  the  normal  eye,  which  is  due  partly  to  the  distance  of  the 
correcting  glass  from  the  eye  (see  page  153),  partly  to  the  fact 


REGULAR  ASTIGMATISM  157 

that  the  cornea  very  frequently  retains  a  certain  degree  of  ir- 
regularity after  extraction.  What  we  have  said  of  the  extrac- 
tion of  cataract  applies  also,  but  in  a  much  less  degree,  to 
iridectomy  and  other  operations  performed  on  the  cornea. 

72.  Keratoconus. — Apart  from  post-operative  cases,  we  meet 
the  highest  degrees  of  corneal  astigmatism  in  cases  of  keratoconus. 
(i)  The  apex  of  the  cone  does  not  generally  coincide  with  the 
visual  line,  which  gives  rise  to  a  strong  astigmatism,  the  direction 
of  which  varies,  following  the  direction  of  the  apex  of  the  cone. 
We  observe  at  the  same  time  that  the  images  of  the  mires  are 


Fig.  84. — Keratoscopic  images  of  a  case  of  keratoconus. 

very  irregular.  By  removing  the  prism  and  placing  the  kerato- 
scopic  disc  in  its  place,  we  easily  find  the  direction  of  the  look 
which  brings  the  apex  of  the  cone  into  the  axis  of  the  ophthal- 
mometer;  we  then  see  the  image  of  the  keratoscopic  disc  quite 


,(1)  The  expression  "keratoconus"  is  not  very  happy;  the  form  of  the  cornea 
approaches  in  these  cases  that  of  a  hyperboloid ;  we  know,  indeed,  that  this  body 
closely  resembles  a  cone  with  rounded  apex. 


158  PHYSIOLOGIC  OPTICS 

small  and  frequently  regular,  round  or  oval;  in  every  other 
position  its  form  is  ovoid  (fig.  84). — The  cases  which  Javal 
had  first  described  under  the  name  of  decentered  eyes,  because 
he  thought  their  deformity  depended  on  an  unusual  size  of  the 
angle  a,  were  affected  with  a  light  degree  of  keratoconus,  as  he 
has  since  acknowledged.  Outside  of  cases  of  keratocnus,  we 
quite  frequently  meet  cases  in  which  the  images  of  the  mires  or 
of  the  keratoscopic  disc  present  more  or  less  pronounced  ir- 
regularities, for  example,  in  consequence  of  old  lesions  of  the 
cornea.  Frequently,  however,  we  still  succeed  in  making  an 
ophthalmometric  measurement  which  may  give  information  use- 
ful for  the  choice  of  a  cylinder. 

73.  Symptoms  of  Astigmatism. — The  most  important  symptom 
of  astigmatism  is  the  diminution  of  visual  acuity,  which  is  a 
consequence  of  the  want  of  distinctness  of  the  image.  Generally 
the  images  are  a  little  deformed,  but  astigmatic  patients  are 
accustomed  to  this  deformity  and  take  no  notice  of  it. 

ASTHENOPIA  OF  ASTIGMATIC  PATIENTS. — On  account  of  their 
diminished  acuity  astigmatic  persons  are  obliged  to  bring  objects 
near  them  for  the  purpose  of  obtaining  larger  retinal  images. 
They  are,  therefore,  obliged  to  accommodate  more  than  other 
persons,  which  is  in  itself  a  cause  of  astigmatism.  But  there 
are  yet  other  reasons  for  it. 

It  may  be  asked  how  astigmatic  persons  see,  that  is  to  say, 
what  part  of  the  interfocal  distance  is  it  that  they  bring  pre- 
ferably on  the  retina.  Following  Sturm  it  was  believed  that,  in 
cases  in  which  they  have  their  choice,  they  prefer  to  use  the 
circle  of  diffusion  so  as  to  see  all  the  outlines  with  the  same 
degree  of  confusion.  According  to  later  researches  (Javal)  it 
is  the  vertical  focal  line  that  they  use  preferably.  There  are 
several  reasons  for  this  preference:  one  is  that  it  is  much  more 
important  in  reading  to  see  the  vertical  lines  distinctly,  the  legi- 
bility of  the  letters  depending  especially  on  the  distinctness  with 
which  the  vertical  lines  are  seen.  Another  reason  is  the  im- 
portance which  vertical  outlines  have  for  binocular  vision.  If 
one  sees  only  the  horizontal  lines,  there  is  nothing  to  indicate 


REGULAR  ASTltlSM  159 


for  what  distance  the  eyes  must  converge.  For  want  of  being 
able  to  use  the  vertical  focal  line  astigmatic  persons  have  re- 
course to  the  horizontal  line,  but  very  rarely  to  the  intermediary 
part. 

In  cases  of  astigmatism  with  the  rule,  the  degree  of  accommo- 
dation to  be  used  depends,  therefore,,  on  the  meridian  of  least 
refraction.  Any  one  having  compound  hypermetropic  astig- 
matism, simple  hypermetropic  astigmatism  or  mixed  astigmatism 
is,  therefore,  in  the  same  situation  as  a  hypermetrope  ;  he  has 
the  same  reasons  for  having  accommodative  asthenopia.  Per- 
sons having  myopic  astigmatism  with  the  rule  or  against  the 
rule  (if  it  is  not  combined  with  hypermetropia)  have  less  cause 
to  suffer  from  asthenopia  and  seem,  indeed,  to  suffer  less.  George 
Bull  especially  has  laid  stress  on  this  explanation  of  the  as- 
thenopia of  astigmatic  persons. 

74.  Examination  of  Astigmatic  Persons.  —  When,  on  examin- 
ing1 the  patient  with  spherical  glasses,  we  do  not  find  a  satisfactory 
acuity  we  suspect  astigmatism,  unless  the  explanations  of  the 
patient  give  reason  to  suspect  an  internal  disease  of  the  eye. 
We  then  submit  the  patient  to  ophthalmometric  examination, 
which,  according  to  the  rules  that  we  have  laid  down,  gives  an 
approximate  idea  of  the  direction  and  degree  of  the  subjective 
astigmatism.  If  we  find  a  very  low  degree  with  the  ophthalmo- 
meter  we  may  generally  come  to  the  conclusion  that  the  com- 
plaints of  the  patient  need  not  be  attributed  to  astimgatism.  We 
then  pass  to  the  subjective  examination  ;  make  the  patient  myopic 
two  or  three  dioptrics  and  move  the  star  figure  close  enough  for 
him  to  see  one  of  the  lines  distinctly.  Under  these  circumstances, 
the  patient  sees  distinctly  the  line  which  corresponds  to  the 
meridian  of  greatest  refraction.  The  direction  of  this  line  indi- 
cates, therefore,  the  direction  of  the  axis  of  a  convex  cylinder; 
a  concave  cylinder  must  be  placed  perpendicularly  to  this  direc- 
tion. It  is  rare  to  find  an  appreciable  difference  between  the 
direction  indicated  by  the  ophthalmometer  and  that  thus  found, 
unless  in  the  case  of  a  very  slight  ophthalmometric  astigmatism 
which  can  have  no  bearing,  in  its  position  and  value,  on  the 


ISO  PHYSIOLOGIC  OPTICS 

total  astigmatism.  We  may  then  proceed  to  find  the  cylinder 
which  equalizes  all  the  lines,  but  the  simplest  way  is  to  find 
directly  the  cylinder  which  gives  the  best  visual  acuity :  we  place 
before  the  eye  the  glass  which  corrects  the  spherical  ametropia, 
joining  thereto  the  cylinder  indicated  by  the  ophthalmometer, 
in  the  position  found  by  means  of  the  star  figure.  After  having 
found  how  much  the  visual  acuity  is  thus  improved,  we  try 
whether  a  further  improvement  is  obtained  by  making  the  glass 
rotate  slightly  in  both  directions  and  adding  a  -\-i  and  — I 
cylinder,  being  very  careful  to  place  the  axis  of  the  glass 
parallel  to  that  which  is  already  in  the  frame.  According  as 
the  acuity  gains  by  adding  a  one  dioptry  convex  or  concave 
cylinder,  we  replace  the  glass  of  the  frame  by  the  following 
number,  and  recommence  the  examination.  With  patients  who 
are  good  observers,  or  when  the  astigmatism  is  slight,  we  may 
sometimes  reach  a  greater  degree  of  accuracy,  by  using  a  half- 
dioptry  cylinder.  When  we  have  found  the  weakest  cylinder 
which  gives  the  best  visual  acuity,  we  verify  the  spherical  glass 
by  adding  a  -|-  I  spherical  which  ought  to  diminish  the  visual 
acuity  and  a  —  i  spherical  which  ought  not  to  increase  it. 

After  having  made  the  subjective  examination,  we  examine 
the  patient  with  the  ophthalmoscope.  I  will  mention  farther  on 
the  ophthalmoscopic  signs  of  astigmatism  on  which  great  stress 
was  laid  at  a  time  when  there  were  no  other  objective  signs  of 
this  anomaly;  they  have  become  today  almost  mere  curiosities, 
especially  since  skiascopy  has  assumed  a  merited  importance. 
When  we  make  use  of  it  for  verification,  we  place  the  correcting 
glass  in  a  frame  and  examine  by  skiascopy  whether  the  correc- 
tion is  complete.  We  can  also  use  it  to  find  out  the  direction 
of  the  axis  and  the  value  of  the  astigmatism,  if  we  have  no 
ophthalmometer. 

Skiascopy  with  a  luminous  point  especially  enables  us  to  find 
very  exactly  the  direction  of  the  axis  by  means  of  the  luminous 
band,  mentioned  on  page  141.  In  order  that  the  phenomenon 
may  be  distinct  it  is  necessary  that  the  eye  of  the  observer  be 
placed  in  one  of  the  focal  lines,  and  that  the  mirror  forms  the 
image  of  the  luminous  source  at  the  place  of  the  other  focal 


REGULAR  ASTIGMATISM  161 

line.  The  observer  will  then  see  luminous  the  meridian  at  the 
focus  of  which  he  is.  Thus  if  the  observed  eye  has  a  myopia 
of  2  D.,  combined  with  an  astigmatism  with  the  rule  of  2  D., 
he  will  see  a  horizontal  luminous  band  if  he  is  placed  at  50 
centimeters  and  illuminates  the  eye  with  a  concave  mirror  which 
projects  the  image  of  the  luminous  source  at  25  centimeters. 
To  see  the  band  vertical  he  must  place  himself  at  25  centimeters 
and  examine  with  a  plane  mirror. — Generally  it  is  necessary  to 
dilate  the  pupil. 

There  are  two  points  in  particular  on  which  I  would  lay  great 
stress.  First,  the  importance  of  the  subjective  examination 
which  must  always  have  the  last  word;  it  is  only  in  cases  in 
which  it  is  impossible  to  obtain  information  from  the  patient,  that 
we  can  attempt  to  give  correcting  glasses  according  to  the  data 
furnished  by  the  objective  methods.  The  reason  is  that,  in 
most  cases,  the  correction  of  the  eye  by  a  cylinder  is  not  a  simple 
optic  problem.  Most  frequently  the  astigmatism  is  not  the  same 
in  the  entire  pupillary  space;  that  of  the  exterior  zones  differs 
more  or  less  from  that  of  the  central  zones ;  the  best  correcting 
glass  is  only  a  sort  of  guess,  which  neither  the  ophthalmometer 
nor  skiascopy  can  assume  to  indicate  exactly.  It  is  well  under- 
stood that  these  differences  are  usually  not  great,  especially  in 
the  case  of  persons  who  consent  to  the  correction,  but  they 
suffice,  however,  to  make  the  subjective  examination  indispens- 
able. 

The  other  point  which  I  would  emphasize  is  that  the  prescrib- 
ing of  cylinders  should  not  be  abused.  Since  the  invention  of 
the  ophthalmometer  there  is  too  decided  a  tendency  to  prescribe 
cylinders  as  soon  as  a  diagnosis  of  astigmatism  is  made.  Cylin- 
drical glasses  should  not,  in  my  opinion,  be  prescribed  unless  they 
produce  a  palpable  improvement  of  the  visual  acuity;  the  wear- 
ing of  glasses  is  always  an  annoyance  for  the  patient,  and  cylin- 
drical glasses  more  so  than  any,  as  well  on  account  of  the  diffi- 
culty of  wearing  them  in  eye-glasses  as  on  account  of  the  errors 
in  the  direction  of  the  axis  which  opticians  sometimes  commit, 
the  difficulty  of  replacing  a  broken  glass,  etc. 


162  PHYSIOLOGIC  OPTICS 

If  there  are  several  cylinders  which  give  the  same  acuity  it 
is  best  to  choose  the  weakest.  If  there  is  astigmatism  of  only 
one  eye,  we  may  allow  the  patient  to  say  whether  he  will  have 
it  corrected  or  not;  generally  he  does  not  gain  much  by  the  cor- 
rection except  in  cases  where  there  is  a  tendency  to  strabismus. 

If  we  combine  two  cylinders  of  the  same  strength  by  placing 
the  axes  parallel,  they  act  like  a  cylinder  twice  as  strong;  if 
we  place  the  axes  perpendicularly  to  each  other,  they  act  like  a 
spherical  glass,  and  if  the  axes  form  an  acute  angle  with  each 
other  the  effect  is  the  same  as  that  of  a  sphero-cylindrical  com- 
bination, the  spherical  and  cylindrical  strength  of  which  vary 
with  the  angle.  As  we  can  obtain  no  other  effect  with  two 
cylinders  than  with  one  cylinder  combined  with  a  spherical  glass, 
the  bi-cylindrical  glasses  are  now  abandoned. 

The  variable  cylindrical  lens  of  Stokes  was  composed  of  one 
cylinder  which  remained  fixed  and  another  which  could  be  ro- 
tated; we  thus  obtained  a  variable  cylindrical  effect,  but  the 
instrument  had  this  disadvantage  that  the  direction  of  the  axis 
varied  also.  Javal  remedied  this  by  making  the  two  cylinders 
rotate  in  opposite  directions;  but,  in  spite  of  this  improvement, 
the  lens  of  Stokes  has  never  been  of  any  practical  utility,  because 
of  the  spherical  effect  which  varies  at  the  same  time  as  the 
cylindrical,  (i) 

We  can  always  obtain  the  effect  of  a  given  sphero-cylindrical 
combination  with  the  cylinder  of  contrary  sign,  by  changing  the 
spherical  glass.  A  +5  spherical  combined  with  a  -[-3  cylindrical 
is  thus  equivalent  to  a  -f-8  spherical  with  a  — 3  cylindrical. 
Really,  there  is  need,  therefore,  of  only  one  kind  of  cylinder; 
there  is  also  now  a  tendency  to  prescribe  only  concave  cylinders 
which  are  combined  with  convex  sphericals  to  obtain  the  effect 
of  convex  cylinders.  By  placing  the  cylinder  on  the  side  of  the 
eye  we  thus  obtain  a  slight  periscopic  effect. 

Periscopic  glasses,  which  were  invented  by  Wollaston,  are  con- 


(1)  [This  last  defect  has  been  overcome  in  the  optometer  of  the  translator. 
In  this  instrument  two  spherical  lenses  are  so  moved  that  the  spherical  effect, 
produced  by  the  rotaion  of  the  two  cylinders  is  always  neutralized  by  the  con- 
trary spherical  effect  of  the  two  spherical  lenses.  Thus  a  purely  cylindrical 
action  is  obtained.  See  Annals  of  Ophthalmology,  Vol.  Ill,  No.  1.] — W. 


REGULAR  ASTIGMATISM  163 

cavo  convex  menisci  the  concave  side  of  which  is  next  the  eye. 
Their  advantage  consists  in  this  that  the  peripheral  parts  of 
the  visual  field  appear  more  distinct  because  the  rays  pass 
through  the  glasses  less  obliquely  than  in  the  ordinary  case. 
This  advantage  also  exists  when  the  eye  is  motionless  as  regards 
the  peripheral  directions  of  the  look.  For  some  time  the  attempt 
has  been  made  to  replace  cylindrical  glasses  by  toric  glasses,  one 
of  the  surfaces  of  which  is  cut  as  a  tore,  the  other  as  a  spherical 
surface.  They  have  the  advantage  of  being  periscopic,  but  their 
manufacture  is  difficult  and  up  to  the  present  they  are  not  very 
popular. 

Cases  of  exact  correction  of  astigmatism  are  among  the  most 
agreeable  which  the  oculist  can  meet,  and  it  happens  quite  fre- 
quently that  a  normal  acuity,  or  even  higher  than  normal,  may 
be  obtained.  Frequently  the  acuity  remains  under  the  normal, 
and  there  is  a  certain  number  of  cases  in  which  the  effect  of 
the  glasses  is  nil  or  nearly  so.  Oculists  are  not  in  agreement 
as  to  the  number  of  cases  in  which  a  good  result  may  be  ob- 
tained. Schweigger  says  that,  in  a  considerable  minority  of 
cases  of  astigmatism  the  correction  obtained  by  cylinders  is 
quite  satisfactory.  Other  authorities  are  less  pessimistic. 

Bibliography. — CEuvres  de  Young,  edited  by  Tscherning,  p.  125. — Airy. 
Transactions  of  the  Cambridge  Phil.  Soc.,  1827,  t.  II  et  1849,  t.  VIII.— 
Sturm.  Sur  la  theorie  de  la  vision.  Reports,  1845. — Goulier.  Sur  un 
defaut  assez  commun  de  conformation  des  yeux  et  sur  les  moyens  de 
rendre  la  vue  distincte  aux  personnes  qui  en  sont  attemtes.  Eeports,  1865. 
— Knapp  (H.).  TJeber  die  Asymmetrie  des  Auges  in  seinen  verschiedenen 
Meridiansystemen.  Arch.  f.  Ophth.,  VIII,  2,  p.  185. — Donders  (F.  C.). 
Astigmatismus  und  cylindrische  Gldser.  Berlin,  1862. — Javal  (E.)  in  de 
Wecker.  Traite  des  maladies  des  yeux,  II,  Paris,  1863. — Javal  (E.).  Sur 
le  choix  des  verres  cylindriques,  Ann.  d'oc.,  1863. — Javal  (E.).  Memoires 
d'ophtalmometrie.  Paris,  1891. — Schioetz  (H.).  Ophtalmometrische  und 
optometrische  Untersuchung  von  969  Augen.  Arch.  f.  Augenh.,  1885. — 
Nordenson  (E.).  Recherches  ophtalmometriques  sur  Vastigmatisme  de  la 
cornee.  Ann.  d'oc.,  1883.  Bull  (G.).  L'asthenopie  des  astigmates.  Bull, 
de  la  Soc.  frang.  d'ophtal.,  1892,  p.  128. 


CHAPTER  X 
IRREGULAR  ASTIGMATISM 

75.  General  Kemarks. — When  we  do  not  succeed  in  obtaining 
a  normal  visual  acuity  by  means  of  spherical  and  cylindrical 
glasses,  we  generally  attribute  the  cause  of  this  failure  to  the 
retina — we  diagnose  amblyopia. — Sometimes,  but,  as  a  rule, 
quite  rarely,  the  'diminution  of  visual  acuity  is  attributed  to  an 
irregular  astigmatism,  especially  if  it  is  visible  by  the  deformities 
of  the  ophthalmoscopic  or  skiascopic  images.  But  it  is  probable 
that  the  more  we  will  study  the  optics  of  the  eye,  the  more 
the  diagnosis  of  amblyopia  will  give  place  to  that  of  irregular 
astigmatism,  which  has  served  up  to  the  present  as  the  common 
term  for  all  optic  defects  of  the  eye  other  than  myopia,  hyper- 
metropia  and  regular  astigmatism,  that  is  to  say,  those  which 
we  can  correct  with  test  case  lenses.  For  some  time  past  the 
majority  of  works  which  have  been  published  on  the  optics  of 
the  eye,  have  had  for  their  object  the  improvement  of  the 
methods  used  to  determine  these  defects  as  quickly  and  as 
exactly  as  possible.  There  is  little  probability  that  we  can,  for 
the  moment,  make  progress  of  any  importance  in  this  direction; 
these  methods  are,  at  present,  very  well  developed ;  it  even  seems 
to  me  that  we  bid  fair  to  overstep  the  limit,  in  this  sense  that 
we  can  perceive  a  tendency  to  desire  to  determine  these  defects 
too  exactly.  Quarters  of  a  dioptry  are,  indeed,  superfluous  for 
our  test  cases,  and  even  half  dioptrics  are  only  rarely  indispens- 
able, except  for  very  weak  ametropias.  So  long  as  it  was 
supposed  that  the  refraction  was  the  same  in  the  whole  pupillary 
space,  we  could  imagine  the  possibility  of  determining  this 
refraction  with  great  exactness.  But  since  we  know  that  there 
are  in  nearly  all  eyes  optic  differences  between  the  different 
parts  of  the  pupillary  space,  and  since  these  differences  may 
reach  several  dioptrics,  the  correcting  glass  must  be  regarded 

164 


IRREGULAR  ASTIGMATISM  165 

as  a  sort  of  approximation  which  we  cannot  determine  with 
perfect  exactness.  It  seems  that  the  construction  of  the  eye 
is  such,  that  the  visual  acuity  is  about  2  for  a  perfect  optic  sys- 
tem; but  many  eyes  have  optic  irregularities  which  lower  the 
acuity  to  I,  to  five-sixths,  to  three-fourths  or  still  lower,  and 
these  irregularities  are  frequently  still  more  pronounced  in  as- 
tigmatic eyes,  which  prevents  complete  correction. 

The  study  of  these  irregularities  seems,  therefore,  destined 
to  play  a  certain  part  in  future  works  on  the  optics  of  the  eye. 
As  I  have  already  remarked,  we  can  study  them  with  the  kerato- 
scopic  disc  of  the  Javal  and  Schioeiz  ophthalmometer,  and  we 
can  measure  them  with  the  optometer  of  Young,  which  necessi- 
tates, however,  on  the  part  of  the  observer  a  certain  amount  of 
work  to  accustom  himself  to  the  instrument.  But  the  best 
means  of  studying  these  irregularities  is  the  following. 

76.  Examination  of  the  Eye  with  a  Luminous  Point. — We  have 
already  seen  that  the  first  authors  who  devoted  their  attention 
to  the  question  of  regular  astigmatism,  used  the  luminous  point 
to  find  the  meridians  and  to  judge  of  the  exactness  of  the  cor- 
rection. Later,  the  luminous  point  was  replaced  by  the  star 
figure,  which  is  in  more  common  use  for  finding  the  meridians, 
but  which  gives  information  only  on  the  astigmatism  which  can 
be  corrected  by  a  cylindrical  glass.  The  forms  under  which  a 
luminous  point  is  seen  furnish,  on  the  contrary,  fuller  informa- 
tion: there  is  no  optic  defect  of  the  eye  which  is  not  shown  in 
these  figures,  sometimes,  it  is  true,  under  a  form  which  it  may 
be  difficult  to  interpret.  This  is  why  we  have  undertaken  this 
examination  at  the  laboratory  of  Sorbonne.  As  object  we  use 
a  very  small  opening  (0.2  mm.  to  0.3  mm.),  made  in  a  dark 
screen,  and  on  which  is  concentrated  the  light  of  a  lamp  or 
daylight.  The  patient,  rendered  myopic,  gradually  approaches 
the  luminuous  point  while  observing  the  form  under  which 
the  latter  may  appear.  We  can  also  place  the  patient  at  a  fixed 
distance,  at  one  meter,  for  example,  and  virtually  change  the 
distance  of  the  luminous  point  by  placing  concave  or  convex 
glasses  before  the  eye;  the  patient  must  avoid  as  much  as 


166  PHYSIOLOGIC  OPTICS 

possible  using  his  accommodation.  We  can  thus  examine  the 
form  of  the  refracted  pencil  throughout  its  whole  extent,  for, 
as  far  as  the  question  at  issue  is  concerned,  it  amounts  to  the 
same  whether  the  luminous  point  be  fixed  while  the  retina  is 
displaced,  or  whether,  the  retina  being  fixed,  we  displace  the 
luminous  point.  Most  of  the  time  the  patient  sees  circles  of 
diffusion  presenting  pretty  exactly  the  form  of  the  pupil,  which 
diminishes  according  as  the  luminous  point  approaches  the  focus. 
But  near  the  latter,  in  front  and  behind,  there  is  a  part,  the 
characteristic  part  of  the  pencil,  where  the  circle  assumes  ir- 
regular forms.  The  round  diffusion  spots  are  alike  in  all;  at 
most  we  find  some  slight  differences  due  to  the  form  of  the  pupil, 
to  a  different  distribution  of  the  brightness  of  the  circles,  or  to 
entopic  phenomena  which  I  shall  describe  in  the  following1 
chapter.  But  the  characteristic  part  of  the  pencil  differs  so  much 
in  different  persons  that  I  have  never  met  two  eyes  in  which  it 
was  alike,  except,  perhaps,  in  the  two  eyes  of  the  same  person. 


Fig.  85.     Forms  under  which  a  luminous  point  is  seen  by  a  regular  eye. 

After  Eee. 


77.  Different  Forms  of  Irregular  Astigmatism. — We  can  dis- 
tinguish several  groups: 


IEEEGULAE  ASTIGMATISM  167 

i°  In  an  ideal  eye  the  characteristic  part  of  the  pencil  is  re- 
duced to  a  point.  We  sometimes  meet  eyes  which  do  not  differ 
much  from  this  type,  but  they  are  rare,  and  all  have  an  ex- 
ceptional visual  acuity  (fig.  85).  (i)  It  is  besides  clear  that, 
all  things  equal,  the  better  the  eye  the  shorter  the  characteristic 
point  of  the  pencil. 

23°  Eyes  regularly  astigmatic  should  see  figures  similar  to 
those  of  figure  77,  but  eyes  so  regular  scarcely  exist.  In  low 
degrees  of  astigmatism  we  scarcely  ever  have  distinct  focal  lines, 
and  in  strong  degrees,  where  the  focal  lines  are  clearer,  irregu- 


Fig.  86.    Kegular  astigmatism  with  spherical  aberration.    After  Eee. 

larities  appear  when  the  astigmatism  is  approximately  corrected 
by  a  cylinder.  The  most  regular  astigmatic  patients  frequently 
see  forms  analogous  to  those  of  figure  86.  The  focal  lines  are 
thicker  at  the  middle  and  the  interfocal  diffusion  spot  is  not 


(1)  Figures  85,  86,  87,  89,  90,  91,  92  are  borrowed  from  a  work  which  M.  R6e 
compiled  at  the  laboratory  of  the  Sorbonne  (Undersoegelse  af  Oeiet  med  et  lysende 
Punct,  Copenhagen,  1896)  and  which  has  the  shape  of  a  small  atlas  showing 
the  forms  under  which  the  eye  sees  a  luminous  point.  But  the  question  is  far 
from  being  exhausted,  and  it  would  be  desirable  that  some  one  should  again  take 
it  up  in  a  clinic.  With  some  exceptions,  the  eyes  of  the  persons  examined  by 
If.  R6e  were  what  we  call  normal  eyes ;  but  it  is  especially  astigmatic  persons, 
whose  vision  does  not  improve  with  cylinders,  that  should  be  examined. 


168 


PHYSIOLOGIC  OPTICS 


Pig.  87. — Figures  of  a  luminous  point  obtained  by  combining  an  ordi- 
nary strong  spherical  lens  with  a  cylindrical  lens  (astigmatism  with 
spherical  aberration).  After  R6e. 


Kg.  88. — A,  forms  which  a  luminous  point  presents  to  my  right  eye 
(obliquity  in  one  meridian,  the  vertical). — B,  appearance  of  the  same 
figures  if  I  cover  the  lower  half  of  the  pupil. — C,  appearance  of  the 
figures  if  I  cover  the  upper  half  of  the  pupil. 

The  figures  a  correspond  to  a  distance  of  60  centimeters;  the  figures 
b  to  1  meter;  the  figures  c  to  1.50m  and  the  figures  d  to  infinity. 


IEEEGULAR  ASTIGMATISM 


169 


circular,  but  in  the  form  of  a  lozenge.    These  forms  are  due  to 
the  combination  of   a  regular  astigmatism  with  a  quite  pro- 


Fig.  89. — Eye  with  double  obliquity.    After  E€e. 

nounced  spherical  aberration,  for  we  can  obtain  forms  wholl} 
analogous  with  a  combination  of  a  -(-20  sph.  with  a  -\-6  cyl.  of 


Fig.  90. — Figures  of  the  left  eye  of  M.  E6e  (Obliquity  in  one  meridian, 
the  vertical).    Curved  focal  line. 


170  PHYSIOLOGIC  OPTICS 

our  test  cases  (fig.  87).  It  is  for  this  reason  that  one  is  obliged 
to  use  an  aplanatic  lens  to  obtain  figures  of  pure  astigmatism. 
In  the  more  irregular  eyes  we  can  generally  find  figures  which 
represent  more  or  less  perfectly  the  focal  lines,  that  is  to  say, 
there  are  two  planes  where  the  figures  are  more  or  less  elongated 
so  that  their  two  long  axes  are  perpendicular  to  each  other;  but 
these  figures  are  far  from  being  linear. 


Fig.  91. — Curved  focal  line.    After  Eee. 

3'°  It  is  not  rare  for  the  optic  system  of  the  eye  to  affect  a 
certain  obliquity,  so  that  the  figures  are  symmetrical  in  relation 
to  a  single  axis  (and  not  in  relation  to  two  axes,  as  in  regular 
astigmatism).  It  is  so  in  the  case  of  my  right  eye  (fig.  88)  and 
also  in  that  of  M.  Ree  (fig.  90).  These  figures  are,  up  to  a 
certain  point,  analogous  to  those  which  are  obtained  with  a  lens 
placed  obliquely. 


IEEEGULAR  ASTIGMATISM  171 

4°  Frequently  we  discover  an  obliquity  in  the  two  directions 
perpendicular  to  each  other,  so  that  the  figures  are  not  sym- 
metrical at  all  (fig.  89). 

5°  An  anomaly  which  is  not  at  all  rare  consists  in  a  certain 
curvature  of  the  focal  lines,  due  probably  to  the  fact  that  the 
principal  meridians  of  the  cornea  show  an  analogous  curvature 
(figs.  90,  91). 


Fig.  92. — Irregular  eye  (Diplopia).    After  Eee. 

6°  We  quite  frequently  meet  more  irregular  figures,  those 
for  instance  of  figure  92,  belonging  to  an  eye  which  has  a  rather 
pronounced  diplopia. 

78.  Eules  for  Analyzing  the  Figures  of  the  Luminous  Point. — 

The  figures  are  sometimes  quite  difficult  to  analyze.     Here  are 
some  directions  for  this  analysis: 

i°  We  can  always  decide  whether  a  part  of  a  figure  is  formed 
by  crossed  rays  or  not,  by  covering  a  part  of  the  pupil.  If  it  is 
the  homonymous  part  of  the  figure  which  disappears,  this  part 
is  formed  by  rays  which  have  already  crossed  the  axis  before 
reaching  the  retina;  if  it  is  the  heteronymous  part  which  dis- 
appears, the  rays  have  not  yet  crossed  the  axis. — Sometimes  we 


172  PHYSIOLOGIC  OPTICS 

can  with  advantage  use  cobalt  glass   (see  page   134)    for  this 
analysis. 

2°  If  the  luminous  point  is  beyond  the  punctum  remotum,  and 
if  the  observer  notices  a  concentric  brightness  on  a  part  of  the 
diffusion  spot,  this  part  corresponds  to  a  less  refracting  part 
than  the  remainder  of  the  pupil;  for,  the  focus  of  this  part  is 
nearer  the  retina  and  its  rays  are,  consequently,  less  dispersed. 

3°  If,  within  the  focus,  the  figures  are  elongated  in  one  direc- 
tion, downwards  for  example,  they  are  elongated  in  the  same 
direction  beyond  the  focus,  and  the  eye  is  more  refracting  in 
this  direction.  Thus  in  figure  95,  A,  in  which  the  lower  part  of 
the  surface  is  supposed  to  be  more  refracting,  the  part  of  the 
cone  situated  above  the  axis  is  everywhere  larger.  The  dif- 
fusion spots  are  seen  elongated  downward  (fig.  88). 

4°  The  aberroscopic  phenomena  (page  123)  always  tell  us  in 
what  direction  the  refraction  increases  or  diminishes,  starting 
from  the  center  of  the  pupil. 

Finally  the  optometer  of  Young  permits  a  more  exact  analysis 
of  these  irregularities. 

Let  us  take,  for  example,  my  right  eye  (fig.  88),  and  see 
how  we  can  use  these  rules  to  analyze  the  figures.  We  observe 
that  the  upper  part  of  the  figure  d,  A,  seen  at  infinity,  has  a 
greater  brightness  than  the  lower  part.  On  covering  the  upper 
half  of  the  pupil,  this  part  disappears,  while,  if  we  cover  the 
lower  half  of  the  pupil,  this  part  does  not  change.  We  conclude 
from  this,  following  rule  i°,  that  the  whole  figure  is  formed 
by  rays  that  have  crossed  the  axis,  that  is  to  say,  that  the  whole 
pupillary  space  is  myopic,  and,  following  rule  2°,  that  the 
upper  part  is  much  less  myopic  than  the  remainder. — If  I  move 
nearer  up  to  1.50  m.  from  the  luminous  point,  I  see  the  figure 
c  which  resembles  a  luminous  T  written  in  a  less  luminous  half 
circle.  If  I  cover  the  upper  half  of  the  pupil,  tire  vertical  stroke 
disappears  and  the  horizontal  stroke  becomes  weaker.  We  con- 
clude from  this,  following  rule  i°,  that  the  vertical  stroke  is 
formed  by  rays  which  have  not  yet  crossed  the  axis.  The  point 
situated  at  1.50  m.  is,  therefore,  already  situated  within  the 


1HREGULAE  ASTIGMATISM 


173 


far  point  of  this  part,  while  it  is  situated  beyond  the  far  point 

of   the   lower   part.     All   the   figures   are 

elongated    downwards,    which   also    shows 

(following  rule  3°)  that  the  pupil  is  more 

refracting  below.    The  lines  of  the  aberro- 

scope  are  convex  towards  the  middle,  below 

and  towards  the  two  sides,  while  they  are 

straight    or   slightly   concave   towards   the 

middle  above  (fig.  93),  which  shows  that   Fig.  93. — Aberroscopk 

the  refraction  diminishes  towards  the  peri-       Phenomena    of    my 

,    .  .  right  eye. 

phery    above    and   increases    in    the   three 

other  directions. — Finally  we  find,  by  measuring  with  the 
optometer  of  Young,  the  refraction  indicated  by  the  diagram 
(fig.  94,  A).  The  measurements  confirm  the  other  observations, 
unless  it  be  that  they  disclose  a  slight  degree  of  hypermetropia 
near  the  upper  border  of  the  pupil,  which  had  escaped  attention 
in  the  analysis  of  the  figures.  It  follows  that  the  course  of 


•rally  M«.7S 


M.t  1  Nasally    Temporally 


Fig.  94. — A,  Diagram  of  the  variations  of  refraction  in  the  pupil  (dilated) 
of  my  right  eye. — B,  diagram  of  the  refraction  in  the  pupil  of  Demi- 
cheri:  the  dotted  circle  indicates  the  normal  pupil,  the  full  circle  the 
dilated  pupil. 

the  rays  must  be  nearly  as  I  have  illustrated  them  in  figure  95 ; 
A  corresponds  to  the  vertical  meridian,  B  to  the  horizontal 
meridian ;  the  place  marked  2  corresponds  to  figure  88,  c. 

As  to  the  means  to  use  for  the  correction  of  these  defects,  they 


174 


PHYSIOLOGIC  OPTICS 


still  remain  to  be  discovered.  The  only  information  we  can  give 
for  the  present  is  that  the  forms  mentioned  under  rule  3°  could 
probably  sometimes  be  corrected  more  or  less  effectively  with 
glasses  placed  obliquely. — Contact  glasses  could  evidently  correct 
the  greater  part  of  these  defects,  which  reside  especially  in  the 


Fig.  95. — Course  of  the  rays  in  my  right  eye:  A,  in  the  vertical  meridian 
(obliquity);  B,  in  the  horizontal  meridian  (spherical  aberration). 

cornea.  As  the  cornea  scarcely  tolerates  contact  Sulzer  caused 
to  be  cut  similar  glasses,  which  are  furnished  with  a  rim  by 
which  they  are  supported  on  the  sclera.  Under  this  form,  con- 
tact glasses  are  easier  to  wear,  but  they  seem  nevertheless  to 


IRREGULAR  ASTIGMATISM  175 

cause  a  certain  annoyance,  which  will  probably  prevent  their 
use,  except  in  special  cases. 

Bibliography. — Tscherning  (M.).  Die  monochromatischen  Abweichun- 
gen.  Zeitschrift  f.  Psych,  u.  Physiol.  der  Sinnesorg.,  IV,  p.  456. — R6e 
(O.  M.).  Undersoegelse  af  Oeiet.  med  et  lysende  Purikt.  (Danois).  Copen- 
hagen, 1896. 


CHAPTER  XI 
ENTOPTIC  PHENOMENA 

79.  Manner  of  Observing  Entoptic  Phenomena. — When  we  ap- 
proach a  luminous  point,  the  circle  of  diffusion  to  which  it  gives 
rise  increases  in  size.  At  the  moment  when  the  luminous  point 
is  at  the  anterior  focus  of  the  eye,  the  rays  are  parallel  after 
refraction,  and  the  circle  of  diffusion  is  the  size  of  the  pupil; 
on  approaching  nearer  to  it,  the  circle  still  increases. 

In  these  circumstances  we  observe  entopic  phenomena,  that 
is  to  say,  shadows  which  the  corpuscles  situated  in  the  refracting 
media  of  the  eye  project  on  the  retina.  If,  instead  of  a  point, 
we  use  a  larger  luminous  source,  the  cone  of  the  shadow  be- 
comes too  short  to  reach  to  the  retina,  except  the  object  is  very 
near  the  latter.  Another  way  of  observing  entoptic  phenomena 
consists  in  placing  ourselves  at  a  great  distance  and  observing 
the  luminous  point  through  a  strong  convex  lens.  In  this  case 
the  displacements  of  the  shadows  take  place  in  the  direction 
contrary  to  that  which  we  are  going  to  point  out  later. — Among 
the  entoptic  observations  I  shall  cite  the  following: 

i°  The  luminous  spot  is  limited  by  the  shadow  of  the  border 
of  the  iris;  we  can  thus  study,  therefore,  the  irregularities  of 
the  latter.  The  pupillary  contraction  is  very  well  observed  on 
opening  or  covering  the  other  eye. 

2°  We  very  frequently  see  small  circles  the  centers  of  which 
are  bright,  and  which  have  an  apparent  motion  from  above 
downwards,  depending  on  the  winking  of  the  eyelids.  They 
are  produced  by  small  specks  on  the  anterior  surface  of  the 
cornea,  and  which  move  in  a  contrary  direction  (fig.  96). 

3°  On  winking  the  eyes  we  produce  transverse  striae,  due 
probably  to  the  wrinkles  of  the  epithelial  layer.  If  we  wink 
for  some  time,  for  example  when  keeping  one  eyelid  closed 
while  working  with  a  microscope,  or  as  artists  frequently  do  in 

176 


ENTOPTIC  PHENOMENA 


177 


order  to  obtain  a  better  idea  of  the  entire  impression  of  a  land- 
scape, we  can  produce  striae  which  last  for  several  hours  and 
give  rise  to  a  very  marked  diplopia  of  the  horizontal  lines  (fig. 
97) .  George  Bull  especially  has  studied  this  question ;  according 


Fig.  97. — Striae  produced  by  winking 
the  eyelids.    (After 


Fig.  96 
After  Helmholtz. 


to  him  the  phenomena  are  specially  pronounced  after  reading 
for  a  long  time  in  the  horizontal  position,  and  give  rise  to  a 
peculiar  annoyance  which  he  has  named  tarsal  asthenopia. 

4°  On  winking  the  eyelids  while  looking  at  a  distant  luminous 
point,  we  observe  long  striae  which  run  upwards  and  downwards 
from  the  point.  These  striae  are  due  to  the  layer  of  tears  which 


Fig.  98. — Prismatic  effect  of  the  layer  of  tears. 

is  in  the  conjunctival  sac,  and  which,  near  the  border  of  the 
eyelids,  assumes  the  form  of  a  prism  with  a  concave  surface 
(fig.  98).  This  prism  deflects  the  rays  which  meet  it,  and,  as 
its  surface  is  concave,  the  parts  placed  near  the  border  of  the 


178  PHYSIOLOGIC  OPTICS 

eyelid  act  as  a  stronger  prism,  which  causes  greater  deflection 
of  the  rays:  it  is  for  this  reason  that  we  see  a  stria  and  not 
simply  a  second  image  of  the  luminous  point.  The  upper  eyelid 
deflects  the  rays  upwards ;  it  produces,  therefore,  the  striae  which 
we  see  directed  downwards.  In  fact,  if  we  lower  a  screen 
placed  near  the  eye,  it  is  the  stria  directed  downwards  which 
disappears  first.  This  phenomenon  is  not,  porperly  speaking, 
an  entoptic  phenomenon,  but  I  mention  it  here  because  of  its 
resemblance  to  those  mentioned  under  N'o.  3°. 

5°  If  we  rub  the  eye,  the  luminous  spot  presents  a  speckled 
appearance,  due  to  irregularities  of  the  cornea;  this  appearance 
soon  disappears  (fig.  99). 

6°  We  sometimes  observe  small  round  discs,  sometimes  bright 
and  surrounded  with  a  black  border,  sometimes  dark  with  a 
bright  (fig.  100),  sometimes  dark,  with  somewhat  more  lumin- 
quently  see  also  the  star  figure  of  the  crystalline  lens,  sometimes 
bright  (fig.  100),  sometimes  dark,  with  somewhat  more  lumin- 


Fig.  99. — Speckled  appearance  of  the  ent-  After  Helmlioltz. 

optic    field     produced     by    rubbing    the  Fig.  100. 

cornea.     (After  George  Bull}. 

ous  borders.  The  crystalline  opacities  are  outlined  in  the  spot 
with  great  distinctness.  Ah  intelligent  patient  can  thus  follow 
step  by  step  the  development  of  his  cataract,  as  we  can  see  on 
the  drawings  which  M.  Darier  has  just  published  (fig.  101). 


ENTOPTIC  PHENOMENA  179 

7°  Nearly  every  one  sees  objects  situated  in  the  vitreous  body; 
they  become  partly  visible  without  further  aid  by  simply  looking 

at  the  sky,  that  is  when  they  are  very 
near  the  retina.  They  are  sometimes 
mobile,  sometimes  fixed,  but  presenting 
in  the  latter  case  an  apparent  motion. 
If,  for  example,  the  shadow  is  seen  a 
little  above  the  point  of  fixation,  the 
patient  looks  a  little  higher  in  order  to 
fix  it;  but  as  the  shadow  is  always  seen 
above  the  point  of  fixation,  it  continues 

Fig.    101. — Incipient  cata-  to    direct    the    visual    line    higher    and 
met,     seen     entoptically.  hi  h          and    the    shadow    aj  flees 

(After  Darier.)  °  . 

before  the  look,  for  which  reason  the 

name  muscce  volit antes  has  been  given  to  this  phenomenon.  To 
make  certain  whether  the  motion  is  apparent  or  real,  we  can 
look  at  the  sky  through  a  window,  on  which  we  select  a  mark 
in  order  to  assure  fixation ;  after  having  made  a  rapid  movement 
with  the  look,  we  fix  this  point.  If  the  corpuscle  is  fixed,  it 
should  then  remain  motionless,  but  most  frequently  we  see  it 
descend  slowly  which  indicates  that  the  corpuscle  really  ascends. 

8°  We  may  use  entoptic  observation  to  study  slight  displace- 
ments of  the  eye  as  a  whole,  which  it  is  very  difficult  to  observe 
otherwise.  To  this  end  I  have  had  constructed  a  small  instru- 
ment, the  entoptoscope  (fig.  ioia).  It  consists  of  a  small  plate 
of  wood  which  we  take  between  the  teeth;  on  the  plate  is  fixed 
a  rod  which  carries  a  plate  of  copper  having  the  form  of  the 
cap  of  a  sphere.  In  the  middle  is  pierced  a  very  fine  opening 
(i/io  mm.),  which  is  on  a  level  with  the  eye.  In  the  concavity 
of  the  cap  are  stretched  two  threads,  one  horizontal  and  one 
vertical,  placed  in  the  form  of  a  cross  and  forming  cords  with 
the  cap.  When  we  take  the  instrument  between  the  teeth  and 
look  towards  the  sky  we  see  the  entoptic  field  occupied  by  the 
cross  which  is  greatly  enlarged.  We  select  a  point  in  the  cross 
as  a  fixation  point.  The  position  of  the  cross  is  thus  invariably 
dependent  on  that  of  the  head;  if  therefore,  in  given  circum- 


180 


PHYSIOLOGIC  OPTICS 


stances,  we  observe  a  displacement  of  the  cross  in  the  entoptic 
field,  it  is  because  it  is  the  latter,  that  is  to  say  the  eye,  which 

suffers  the  displacement.  We 
can  thus  prove  that  the  eye  is 
slightly  displaced,  a  little  up- 
wards when  we  wink  the  eye- 
lids, a  little  downwards  when 
we  open  the  eye  very  widely. 
When  we  lean  the  head  to 
one  side  the  eye  undergoes  a 
slight  displacement  in  the  di- 
rection of  the  weight,  etc. 
The  phenomena  are  especially 
striking  when  we  instill  eser- 
ine,  because  the  field  is  then 

\  very  small.  The  displacement 

of  the  cross  may  then  reach 
a  fourth  or  a  third  of  the  en- 
tire extent  of  the  field. 


Fig.  10 la. — Entoptoscope.     a,  plan- 
chette  of  wood;  6,  rod;  c,  copper 
plate,  perforated;  d,  thread. 


80.  Analysis  of  Entoptic 
Phenomena. 

a).  OBSERVATION  OF  THEIR 
PARALLAX  ( Listing ) .  —  By 
fixing  different  points  of 

the  entoptic  field,  we  observe  that  the  entoptic  phenomena  are 
displaced  in  the  field.  If  the  corpuscle  which  gives  rise 
to  the  shadow  is  behind  the  pupillary  plane,  the  shadow 
moves  in  the  same  direction  as  the  visual  line  (fig.  102,  a,  b). 
Taking  the  position  b,  the  visual  line  is  directed  upwards;  the 
shadow  has  descended  to  near  the  lower  border  of  the  field,  but 
seems  to  have  ascended  (by  the  projection  outwards).  It  is 
easy  to  see  that  we  have  the  contrary  parallax  if  the  object 
is  in  front  of  the  pupillary  plane,  and  that  it  disappears  if  the 
object  is  in  this  plane.  As  the  movement  is  greater  in  propor- 
tion as  the  object  is  more  removed  from  the  pupillary  plane,  we 


ENTOPTIC  PHENOMENA 


181 


can  thus  form  an  approximate  idea  of  the  position  of  the  cor- 
puscle. 


Fig.  102. — Parallax  of  the  entoptic  phenomena. 

b).  MEASUREMENT  OF  THE  DISTANCE  OF  THE  CORPUSCLE  FROM 
THE  RETINA  (Breivster,  Donders  and  Doncan). — To  measure 
this  distance  Brewster  proposed  to  use  two  luminous  points.  We 
then  see  two  circles  of  diffusion  which  partly  overlap,  arid  each 
corpuscle  produces  two  shadows.  Wie  measure  the  distance 
between  the  two  shadows  of  the  same  object  and  the  diameter 
of  the  free  part  of  one  of  the  circles  DE  (fig.  103)  ;  the  ratio 
between  these  two  measurements  is  equal  to  the  ratio  between 
the  distance  of  the  object  from  the  retina  and  that  of  the  pupil 
from  the  retina. 

Let  A1  and  B  (fig.  103)  be  two  luminous  points  which  must 
be  in  the  anterior  focal  plane  of  the  eye,  d  the  middle  of  the 
pupil,  o  the  object,  p  and  p^  the  shadows  and  c  and  cl  the  centers 
of  the  circles  of  diffusion.  Since  the  points  are  in  the  focal 
plane,  dc  is  parallel  to  op  and  dc1  to  oplt  therefore:  &L  =  -^ 
and  figure  103  b  shows  that  cc1=DE=R-\-  a  if  R  is  the  radius 
of  the  circle  of  diffusion. — We  can  make  measurements  by  using 
as  a  luminous  source  a  sheet  of  white  paper  strongly  illuminated. 
We  look  through  two  stenopaic  openings  towards  this  sheet 


182  PHYSIOLOGIC  OPTICS 

and  we  notice  the  places  where  the  shadows  are  projected  as 
well  as  the  borders  of  the  circles  (Bonders).  Doncan  made  the 
measurements  a  double  vue  by  comparing  the  entoptic  phenomena 
with  a  scale  seen  with  the  other  eye. 


Fig.   103. — 'Determination  of  the  position   of  an  entoptic  object.     After 

Brewster. 

c).  EXAMINATION  OF  THE  REFRACTION  OF  THE  OBJECT. — So 
far,  we  have  treated  the  entoptic  phenomena  as  shadows,  and 
the  objects  which  produce  them  as  opaque  bodies.  Most  fre- 
quently, this  is  not  the  case,  as  they  are  more  or  less  transparent ; 
but  their  refraction  is  different  from  that  of  the  surrounding 
parts,  whether  their  surface  has  a  different  curvature,  or  whether 
their  index  is  different. 

It  is  easy  to  see  (fig.  104)  that  the  more  refracting  objects 
must  concentrate  the  light  so  that  the  entoptic  image  becomes 
luminous  and  surrounded  by  a  dark  border;  this  is  the  case 
with  the  images  of  the  corneal  specks. — On  the  contrary,  if  the 
object  is  less  refracting  than  the  surrounding  parts,  the  image 
is  dark,  with  a  more  luminous  border.  The  difference  is  specially 
marked  in  the  case  of  the  star  figure  of  the  crystalline  lens, 
which,  in  some  people,  appears  dark,  in  others  luminous,  thus 
indicating  that  the  refraction  of  the  corresponding  parts  is 


ENTOPTIC  PHENOMENA 


183 


sometimes  greater,  sometimes  less  than  that  of  the  surrounding 
parts. — If  we  make  the  experiment  by  placing  ourselves  at  a 
great  distance,  and  making  the  eye  strongly  myopic,  we  should 
have  the  phenomena  inverted. 


Fig.  104. — The  drop  on  the  cornea  causes  convergence  of  the  rays  which 
pass  through  it  so  that  we  see  a  luminous  center  surrounded  by  a 
shadow. 


Iii  the  experiment  which  we  have  just  noted  (fig.  104),  the 
dark  border  is  due  to  the  fact  that  part  of  the  rays  which  should 
illuminate  it  are  made  to  converge  towards  the  middle  of  the 
entoptic  image,  by  the  interposition  of  the  corpuscle.  This  border 
is  always  diffuse  and  frequently  somewhat  pronounced;  it  must 
not  be  confounded  with  the  diffraction  ring  which  surrounds 
the  images  along  the  border  of  the  pupil  when  the  luminous 
point  is  very  small.  This  ring,  which  sometimes  may  be  double 
or  triple,  is  always  very  thin  and  very  distinct. 

81.  Entoptic  Observation  of  the  Vessels  of  the  Retina  (Pur- 
kinje). — a).  If,  in  a  dark  room,  we  hold  a  candle  at  some  distance 
from  the  eye  while  we  look  directly  in  front,  we  see  the  retinal 
vessels  greatly  magnified  projected  on  the  dark  portion  of  the 
room.  They  appear  dark  (of  a  deep  blue)  on  a  somewhat  more 
luminous  ground  (orange). — If  we  move  the  candle  towards 
or  away  from  the  visual  line,  the  vessels  seem  displaced  in  the 
same  direction;  if,  on  the  contrary,  we  move  the  candle  around 
the  visual  line,  the  vessels  seem  to  move  in  the  direction  oppo- 
site to  that  of  the  candle.  The  fovea  appears  without  vessels: 
in  my  eye  it  offers  a  kind  of  starlike  appearance;  in  others 


184  PHYSIOLOGIC  OPTICS 

(Burow)  it  appears  as  a  luminous  disc,  limited  by  a  crescent- 
shaped  shadow. 

The  explanation  of  these  phenomena  has  been  given  by  H. 
Miiller.  By  refraction  there  is  formed  at  a  (fig.  105)  a  retinal 
image  of  the  candle;  the  part  of  the  retina  thus  illuminated 
sends  diffuse  light  in  all  directions.  The  vessel  v  intercepts  the 
rays  &v,  so  as  to  form  the  shadow  b  on  the  sensitive  layer  of 
the  retina;  it  is  this  shadow  that  we  see  (the  retina  is  repre- 
sented too  thick  on  the  figure ;  really  the  shadow  is  very  near 
the  vessel).  Illuminated  directly,  the  vessel  also  form  a  shadow 


Fig.  105. — Entoptie  observation  of  the  vessels.     (After  H.  Muller.) 

on  the  sensitive  part  situated  behind  it;  but  this  shadow  is  not 
usually  perceived,  because  it  is  always  formed  at  the  same  place 
(and  because  the  sensitive  layer  has  thus  become  accustomed 
to  it)  or,  perhaps,  because  the  part  of  the  retina  which  is  behind 
the  vessel,  being  always  covered,  is  never  fatigued  and  conse- 
quently remains  much  more  sensitive,  so  that  the  little  light 
which  passes  through  the  vessel  produces  as  strong  an  impres- 
sion on  this  part  as  the  full  light  on  the  remainder  of  the  retina. 

It  seems  that  the  vessels  form  in  ordinary  circumstances 
negative  scotomata,  like  the  spot  of  Mariotte,  although  it  may 
be  difficult  to  observe  them,  except  near  the  papilla,  because  of 
the  instability  of  the  fixation  (see  chap.  X'VIII). 

b).  We  concentrate  with  a  convex  lens  the  light  of  a  flame  on 
the  sclera,  as  far  as  possible  from  the  border  of  the  cornea.  By 


ENTOPTIC  PHENOMENA  185 

bringing  the  focus  somewhat  on  the  sclera,  we  see  dark  vessels 
on  an  orange  ground.  The  vessels  move  in  the  same  direction 
as  the  luminous  focus.  On  concentrating  the  light  on  the  in- 
ternal part  of  the  sclera  we  succeed  in  seeing  the  luminous  focus 
itself  under  the  form  of  a  red  sun  near  the  external  border  of 
the  visual  field. 

The  explanation  is  analogous  to  that  of  the  preceding  case. 
The  light  of  the  image  of  the  flame,  formed  on  the  sclera,  passes 
through  this  membrane  and  the  choroid,  and  disperses  in  the 
interior  of  the  eye  where  it  forms  vascular  shadows  at  unusual 
places. — //.  Miiller  measured  the  distance  ab  (fig.  106),  separat- 
ing two  successive  positions  of  the  luminous  focus,  and  the  dis- 
placement aB  of  the  shadow  of  a  vessel  corresponding  to  this 
displacement  of  the  light.  With  these  data,  he  calculated  that 
the  vessel  should  be  0.17  to  0.33  mm.  in  front  of  the  sensitive 
layer.  This  experiment  seems  to  prove  that  it  is  the  layer  of 
the  cones  and  rods  that  is  the  sensitive  layer,  for  the  distance 
of  the  small  vessels  near  the  macula  from  the  layer  with  the 
cones  is  very  nearly  the  same  (0.2  to  0.3  mm.). 

Another  phenomenon,  also  due  to  the  influence  of  the  light 
which  passes  through  the  sclera  and  the  choroid,  is  observed 
when  we  place  ourselves  near  the  luminous  source,  a  window 
for  exampe,  so  that  one  eye  may  be  illuminated  while  the  other 
is  in  the  shade.  After  a  little  while  we  then  observe,  on  closing 
the  eyes  alternately,  that  the  white  objects  seen  with  the  illumi- 
nated eye  present  a  greenish  tint,  while  they  appear  reddish  to 
the  other  eye.  The  light  which  passes  through  the  sclera  and 
the  choroid  is  colored  red  by  the  blood  of  the  latter  membrane. 
This  red  light  "fatigues"  the  retina  of  the  illuminated  eye,  which 
has  the  effect  of  making  white  objects  assume  a  greenish  tint. 
The  other  eye  sees  them  red  by  contrast. 

When  we  read  in  full  sunlight,  we  sometimees  see  the  letters 
vividly  colored  red.  The  phenomenon  is  probably  of  the  same 
kind  as  the  preceding.  The  red  light,  which  passes  through  the 
membranes  of  the  eye,  comes  to  be  added  to  the  light  which 
passes  through  the  pupil.  It  is  not  sufficiently  great  to  percep- 


186  PHYSIOLOGIC  OPTICS 

tibly  change  the  tint  of  the  white  paper,  brightly  illuminated  by 
the  sun,  but  it  colors  red  the  black  letters,  which  send  back 
only  very  little  of  the  white  light. 

c).  Looking  at  the  sky  through  a  stenopaic  opening,  we  see 
very  distinctly  pictured  the  granulated  ground  and  the  delicate 
vessels  which  surround  the  macula;  but 
the  stenopaic  opening  must  be  kept  in 
continuous  motion,   otherwise  the   phe- 
nomenon disappears.    If  we  look  at  the 
sky  without  the  stenopaic  opening,  the 
shadow  of   the  vessel   is  too   short  to 
reach   the    sensitive    layer.      The    same 
phenomenon     is     frequently     observed 
when    working    with    the    microscope: 
when  we  illuminate  the  field  with  day-      Fig>   106>_Entoptic   ob. 
light,  we  see  the  vessels  by  placing  the         serration   of   the   ves- 
eye  at  the  ocular  and  giving  it  a  to-and-         sels  b7  illumination  of 
fro  motion.    The  muscce  of  the  vitreous 
body  may  also  be  very  well  observed  in  this  way. 

Wihen  making  this  experiment,  as  well  as  the  preceding  one, 
we  sometimes  see  the  vessels  become  luminous;  this  is  due  to 
the  fact  that  the  parts  of  the  sensitive  layer  on  which  the  shadow 
falls,  in  ordinary  circumstances,  are  now  exposed  to  the  light, 
which  acts  much  more  strongly  on  these  parts  than  on  the 
remainder. 

82.  Other  Entoptic  Phenomena. — a).  Looking  towards  the  sky, 
we  very  frequently  see  bright  points  which  seem  to  move  lively 
and  then  to  disappear,  giving  place  to  others  (Purkinje).  The 
phenomenon  is  often  more  pronounced  if  we  look  through  a 
cobalt  glass.  This  phenomenon  is  explained  by  the  pressure 
which  is  exerted  on  the  sensitive  layer  by  a  globule  of  blood 
which  is  stopped  in  a  very  narrow  capillary,  (i) 


(1)  [Another  and  very  probable  explanation  of  this  phenomenon  assumes  that 
we  observe  in  the  little  bright  bodies  some  relatively  empty  capillary  spaces, 
produced  by  small  temporary  local  stoppages  of  the  circulation  in  the  capillaries 
of  the  retina.  See  the  paper  by  the  translator  in  the  Ophthalmic  Record,  Febru- 
ary, 1900.] — W. 


ENTOPTIC  PHENOMENA  187 

b).  By  compressing  the  eye  for  some  time,  we  can  see  the 
retinal  vessels  and  even  notice  the  blood  globules  magnified 
about  50  times.  The  retinal  vessels  appear  bluish;  but,  before 
perceiving  them,  we  see  those  of  the  chorio-capillary  membrane, 
red  on  a  black  ground  (Vierordt,  Laiblin).  It  seems  that  this 
experiment,  which  Young  had  already  made,  would  not  succeed 
with  everybody. 

c).  A  pressure  localized  on  a  small  part  of  the  sclera  gives 
rise  to  a  phosphene  which,  like  every  other  retinal  impression,  is 
projected  in  the  opposite  direction.  Making  the  experiment  in 
darkness,  we  notice  that  the  phosphene  has  the  form  of  a  feebly 
luminous  disc,  surrounded  by  a  bright  border,  corresponding  to 
the  inflection  of  the  retina.  With  very  prominent  eyes  Young 
succeeded  in  producing  a  phosphene  corresponding  to  the 
macula:  exteriro  objects  which  were  in  the  position  of  the 
phosphene  were  still  visible,  but  presented  very  pronounced  de- 
formities.— If  we  exert  on  the  eye  a  pressure  sufficiently  strong 
and  uniform,  the  entire  visual  field  is  darkened  in  consequence 
of  the  anemia  of  the  retina. 

d).  On  making,  in  a  dark  room,  rapid  movements  with  the 
eyes,  we  observe  two  luminous  circles  corresponding  to  the 
places  of  entrance  of  the  optic  nerves  and  due  to  the  traction 
produced  by  these  nerves  during  the  movement. 

e).  On  making  an  effort  of  accommodation  in  a  dark  room, 
we  sometimes  see  a  very  large  luminous  circle,  which  is  attri- 
buted to  the  traction  which  the  ciliary  muscle  exerts  on  the 
interior  membranes  of  the  eye  during  accommodation  ( phosphene 
of  accommodation  of  Czermak).  I  did  not  succeed  with  this 
experiment. 

/).  A  weak  electric  current  makes  visible  at  the  moment  of 
closure  the  dark  papilla  on  a  blue  ground,  if  the  current  is 
ascending;  whitish  blue  on  a  dark  orange  ground  if  the  current 
is  descending:  on  opening  the  current  we  have  the  phenomena 
reversed.  If  the  current  is  strong,  we  see  all  the  colors  of  the 
spectrum  mixed. 

g).  On  looking  towards  the  sky  through  a  Nicol  prism,  we 
see  the  brushes  of  Haidinger,  an  indistinct  cross,  one  of  the 


188  PHYSIOLOGIC  OPTICS 

arms  of  which  is  yellow,  the  other  blue;  the  phenomenon  rotates 
with  the  nicol.  Some  persons  can  see  the  phenomenon,  but  less 
pronounced,  without  a  nicol. 

h).  Phenomena  of  Diffraction  in  the  Eye.  Looking  towards  a 
very  intensely  luminous  point  we  see  it  surrounded  with  an 
infinity  of  very  fine,  many-colored  radiations,  the  whole  of  which 
is  known  under  the  name  of  ciliary  corona.  Its  extent  varies 
with  the  intensity  of  the  luminous  point.  If  the  latter  is  very 
bright  (a  reflected  image  of  the  sun)  the  diameter  of  the  corona 
may  reach  8  degrees  or  more.  The  cause  of  the  phenomenon  is, 
in  all  probability,  to  be  found  in  the  fibrous  structure  of  the 
crystalline  lens. 

Besides  the  ciliary  corona  most  people  see  around  the  entire 
luminous  source  a  somewhat  vivid  diffraction  ring  A,  presenting 
the  colors  in  the  well-known  order:  red  outside,  blue  inside. 
The  diameter  of  the  ring  (blue)  is  about  3  degrees.  The  space 
which  separates  it  from  the  luminous  source  is  filled  with  the 
ciliary  corona. 

Druault  and  Salomonsohn  have  recently  described  a  second, 
larger  ring  B  (6  to  7  degrees  in  diameter),  which  seems  to  ap- 
pear in  every  one  when  the  pupil  is  dilated.  It  presents  the 
colors  in  the  same  order  as  the  first,  but  it  is  more  irregular, 
and  composed  of  radial  striae.  Making  these  observations  with 
monochromatic  light,  the  ciliary  corona  presents  itself  under 
the  form  of  a  luminous  dust,  which  is  concentrated  towards 
the  periphery  so  as  to  form  the  two  rings  which  I  have  just 
described.  Quite  near  the  luminous  source  we  see  one  or  two 
black,  very  fine  rings,  due  to  diffraction  by  the  border  of  the 
pupil. 

The  ring  A  is  probably  due  to  the  epithelial  cells  of  the 
cornea,  and  analogous  to  the  rings  which  we  observe  on  looking 
through  a  glass  plate  covered  with  grains  of  lycopodium.  On 
covering  a  larger  and  larger  part  of  the  pupil  with  a  screen,  we 
see  the  entire  ring  become  indistinct  and  disappear  at  once. 
Schioetz  has  shown  that  on  exposing  the  cornea  to  the  action 
of  distilled  water  for  some  time,  as  in  the  experiment  of  Young, 
page  202,  we  observe  a  pretty  system  of  rings,  the  first  of  which 


ENTOPTIC  PHENOMENA  189 

corresponds  almost  to  the  ring  A.  We  must  note,  however,  that 
Druault,  on  looking  through1  a  dead  cornea,  showed  the  existence 
of  a  ring,  the  dimensions  of  which  scarcely  differed  from  those 
of  the  ring  A,  and  which  was  undoubtedly  due  to  the  endothelium 
of  the  membrane  of  Descemet:  he  could  remove  the  entire 
epithelium  of  the  anterior  surface  without  producing  the  least 
change  in  the  ring,  which  would,  on  the  contrary,  disappear  as 
soon  as  he  touched  the  endothelium. 

The  ring  B,  which  was  previously  described  by  Danders,  is 
due  to  the  crystalline  fibres  which  act  as  a  grating.  If  we  cover 
a  part  of  the  pupil  with  a  screen,  we  see  a  part  of  the  ring  dis- 
appear while  the  remainder  does  not  change.  Druault  succeeded 
in  reproducing  the  phenomenon  with  dead  crystalline  lenses. 

The  rings  which  glaucomatous  patients  see  resemble  these 
rings,  but  are  generally  larger  (10  to  n  degrees).  As  the  size 
of  the  rings  is  inversely  proportional  to  that  of  the  corpuscles 
which  produce  them,  it  is  probable  that  the  origin  of  the  glauco- 
matous rings  is  to  be  found  in  the  deepest  layer  of  the  corneal 
epithelium,  the  cells  of  which  are  much  smaller  than  the  super- 
ficial cells  (Schioetz).  Placing  a  drop  of  blood  in  the  conjunc- 
tival  sac  we  obtain  a  very  pretty  ring  (diameter  7.5  degrees  for 
the  yellow)  surrounded  by  a  second  paler  ring.  The  space 
between  the  first  ring  and  the  light  is  not  black,  as  for  the  other 
rings  here  described,  but  yellowish  or  maroon  (Druault}.  These 
rings  seem  analogous  to  those  sometimes  seen  by  persons  affected 
with  conjunctivitis. 

i).  I  recently  described  a  kind  of  entoptic  phenomenon  which 
I  observed  in  the  following  circumstances.  We  surround  a  lamp 
with  a  transparent  shade,  made  of  some  layers  of  colored  tissue 
paper,  for  example.  We  place  ourselves  at  some  meters  dis- 
tance, and  interpose  an  opaque  screen,  in  which  has  been  cut 
a  vertical  slit,  between  the  lamp  and  the  eye;  the  distance  of 
the  screen  from  the  eye  may  vary  between  30  cm.  and  several 
meters.  We  close  the  left  eye  and  fix  with  the  right  eye  a 
point  on  the  screen,  situated  near  the  right  border  .of  the  slit. 
To  begin,  we  hold  the  head  so  that  the  eye  may  be  in  darkness. 
Then  we  move  the  head  so  that  the  eye  enters  into  the  luminous 


190  PHYSIOLOGIC  OPTICS 

pencil  which  passes  through  the  slit  while  maintaining  fixation 
at  the  same  place.  At  the  same  moment  we  see  the  phenomenon 
appear  under  the  form  of  two  blue  arcs,  feebly  luminous,  but 
bright,  which  go  from  the  slit  towards  the  position  of  the  blind 
spot  by  turning  around  a  fixed  point  (fig.  1060).  The  phenome- 


Fig.  106a. — Entoptie  phenomenon. 

non  lasts  only  a  moment;  an  instant  later  the  arcs  become  nar- 
row, the  interior  which  was  black  is  filled  with  a  blue  glow, 
and  the  whole  disappears,  to  reappear  again  with  the  least 
motion  of  the  eye.  To  see  the  phenomenon  with  the  left  eye 
it  is  necessary  to  fix  the  left  border  of  the  slit. 

According  to  a  communication  from  D.  Crzellitzer  the  phe- 
nomenon was  described  by  Purkinje  in  a  publication  which  I 
have  not  at  my  disposal.  It  seems  very  prevalent;  among  per- 
sons whom  I  have  examined  in  this  regard,  I  have  met  only  a 
single  one  who  has  not  been  able  to  see  it.  The  form  of  the 
arcs  recalls  the  course  of  the  nerve  fibres  at  this  place.  The 
appearance  resembles  that  of  certain  phosphorescent  bodies,  by 
the  bluish  color  and  by  the  impression  which  it  gives  of  being 
feeble  and  yet  bright  at  the  same  time;  we  again  find  the 
same  appearance  for  different  other  phenomena  which  we  ob- 
serve in  darkness,  for  instance  the  after  image  of  Purkinje  (see 
page  292),  the  trace  which  the  impression  of  a  red  coal  leaves 
on  the  retina,  and  so  forth. 


ENTOPTIC  PHENOMENA  191 

Bibliography. — (Euvres  de  Young,  edited  by  Tscherning,  p.  71,  140  and 
168. — Purkinje  (J.  E.).  Beitrdge  zur  Kentniss  des  Sehens,  1819,  p.  89, 
et  neue  Beitrdge,  1825,  p.  115. — Listing  (J.).  Beitrag  zur  physiologischen 
Optik.  Gottingen,  1845. — Doncan  (A.).  De  corporis  vitrei  structure,. 
Utrecht,  1854. — Brewster  (D.).  Transactions  of  the  Eoyal  Soc.  of  Edinb., 
XV,  377. — Muller  (Heinrich).  Verh.  der  med.  physik.  Gesellschaft  zu 
Wurzburg.  IV,  V. — Haidinger.  Ueber  das  directe  Erkennen  des  polar- 
isirten  LicJits  und  der  Lage  der  Polarisationsebene.  Poggend.  Ann.  1844. 
— Darier  (A.).  De  la  possibility  de  voir  son  propre  cristallin  Ann.  d'oc. 
t.  CXIV,  p.  198,  1895. — Schioetz  (H.).  Om  nogle  optisJce  equeskaber  ved 
Cornea.  Christiana,  1882. — Druault  (A.).  Sur  la  production  des  anneaux 
colores  autour  des  flammes.  Arch,  d'ophtalmol.,  Mai,  1898,  et  Compte 
rendu  du  Congres  d'  Utrecht,  1899. — Salomonsohn  (H.).  Ueber  Licht- 
beugung  an  Hornhaut  und  Linse.  Arch.  f.  Anal.  u.  Phys.,  1898.  Tscher- 
ning (M.).  Eine  Selbstbeobachtung.  Kl.  M.  f.  A.  June,  1898. — Tscher- 
ning (M.).  Compte  rendu  du  Congres  d'  Utrecht,  1899. 


CHAPTER  XII 

ACCOMMODATION 

83.  Measurement  of  the  Amplitude  of  Accommodation. — We 
have  defined  the  amplitude  of  accommodation  as  the  difference 
between  the  distances  of  the  far  point  and  the  near  point,  meas- 
ured in  dioptrics.  It  expresses  the  value  of  a  convex  lens  which, 
added  to  the  eye,  would  form  an  image  of  the  near  point  at  the 
position  of  the  far  point. 

For  the  determination  of  the  near  point  it  is  necessary,  on  ac- 
count of  the  relation  between  accommodation  and  convergence, 
which  I  shall  discuss  later,  to  close  the  eye  which  we  are  not 
examining.  In  order  to  reach  the  highest  degrees  of  accommo- 
dation, the  patient  is  sometimes  obliged  to  squint  inwards,  and, 
if  both  eyes  are  open,  the  need  of  seeing  single  will  prevent 
him  from  attaining  the  limit  of  his  accommodation.  In  clinics, 
we  generally  confine  ourselves  to  determining  the  shortest  dis- 
tance at  which  the  patient  can  read  fine  print.  It  is  necessary, 
for  this  determination,  to  use  very  small  letters,  otherwise  the 
patient  may  still  read  them  within  the  near  point,  although  see- 
ing the  letters  only  indistinctly. — Another  method  consists  in 
determining  the  strongest  concave  glass  through  which  the 
patient  can  see  distant  objects  distinctly  (the  table  of  visual 
acuity),  since  the  concave  glass  forms  an  image  of  them  so 
much  nearer  in  proportion  as  it  is  stronger.  We  can  also  use 
optometers,  that  of  Badal  or  of  George  Bull  (i)  for  example. 

The  determination  of  the  near  point  is  always  uncertain,  be- 
cause we  can  never  know  whether  the  patient  makes  a  maximum 
effort  or  not.  It  succeeds  especially  poorly  in  persons  of  little 
intelligence,  in  children,  etc.  Anyhow,  to  determine  it  exactly 
is  generally  of  little  practical  importance;  if  we  desire  an  exact 


(1)  The  optometer  of  Bull  resembles  externally  that  of  Young,  enlarged,  but 
the  principle  is  different.  We  look  through  a  lens  of  6  D.  without  slits,  and  the 
line  is  replaced  by  a  series  of  small  dominoes.  The  patient  must  simply  tell 
the  most  distant  and  nearest  of  these  dominoes  that  he  can  see  distinctly. 

192 


ACCOMMODATION  193 

measurement,  we  can  instil  eserine,  but  we  thus  obtain  an 
amplitude  slightly  higher  than  that  which  the  patient  would 
attain,  even  when  trying  his  best. 

For  scientific  researches  it  may  sometimes  be  important  to 
know  exactly  the  amplitude  of  accommodation.  We  can  then 
determine  it  with  the  optometer  of  Young,  if  the  observer  is 
master  of  his  accommodation,  that  is  to  say,  if  he  can  make 
an  effort  of  accommodation  without  fixing  a  near  object.  If 
not,  the  best  means  is  to  offer  a  hair  in  a  ring,  and  to  see  how 
close  we  can  move  it  to  the  eye  before  it  appears  dim.  We  may 
with  advantage  add  this  ring  to  the  optometer  of  Young. 

The  amplitude  of  accommodation  diminishes  in  a  very  regular 
manner  with  age.  According  to  Bonders,  the  diminution  begins 
to  make  itself  felt  at  the  close  of  infancy.  It  is  so  regular,  at 
least  beginning  at  25  or  30  years,  that  we  can  frequently  deter- 
mine the  age  of  the  patient  to  almost  within  one  or  two  years, 
by  means  of  the  optometer  of  Bull,  for  example.  At  the  age 
of  47  or  48  years  this  diminution  begins  to  manifest  itself  in 
emmetropes,  by  the  appearance  of  presbyopia.  In  hypermetropes 
the  presbyopia  makes  its  appearance  sooner;  it  appears  later  in 
low  myopia,  and  myopes  of  a  high  degree  never  become  pres- 
byopic,  although  the  amplitude  of  accommodation  diminishes 
in  them  as  in  every  one  else.  In  emmetropes  it  is  very  rare  to 
find  an  exception  to  the  rule  laid  down  above,  unless  the  pupil 
is  very  small.  If,  therefore,  a  patient  reads  without  glasses 
when  over  50  or  55  years  old,  he  must  be  myopic,  if  the  pupil 
is  of  the  ordinary  size. 

Presbyopes  do  not  suffer  from  accommodative  asthenopia; 
when  reading  they  are  obliged  to  hold  the  book  farther  away, 
especially  in  the  evening;  the  manner  in  which  they  hold  the 
book,  far  from  their  eyes  and  near  the  lamp,  is  very  character- 
istic. 

As  to  the  choice  of  spectacles,  it  is  clear  that  if  we  fix  on  a 
distance  for  work  of  33  centimeters  we  are  never  obliged  to 
give  to  an  emmetrope  glasses  of  a  greater  strength  than  3 
dioptrics.  But  it  is  frequently  useful,  especially  when  the  acuity 
is  diminished,  to  choose  a  shorter  distance  for  work,  for  ex- 


194  PHYSIOLOGIC  OPTICS 

ample  25  centimeters,  corresponding  to  4  dioptrics.  We  fre- 
quently notice  a  tendency  to  give  somewhat  stronger  glasses, 
which,  however,  cause  only  slight  inconvenience.  Thus,  the 
series 

50  55  60  65  years 

-J-  1  +2  -f  3  -f  4  dioptries 

is,  perhaps,  a  little  strong,  especially  for  high  degrees. 

PARALYSIS  OF  ACCOMMODATION. — Wie  meet  this  disease  es- 
pecially in  children  who  have  had  diphtheria.  If  we  learn  that 
the  child  has  not  been  able  to  read  for  some  time  past,  although 
it  sees  perfectly  at  a  distance,  and  if  we  do  not  find  hyper- 
metropia,  we  may  be  almost  certain  that  it  has  had  diphtheria. 
The  diagnosis  of  paralysis  is  verified  when  the  child  reads  well 
with  the  proper  convex  glasses.  Generally  there  are  no  other 
symptoms  of  ocular  paralysis,  among  others  no  mydriasis.  We 
prescribe  convex  glasses  almost  until  the  recovery,  which  gen- 
erally takes  place  in  a  space  of  two  or  three  months. 

The  second  form  of  paralysis  which  we  occasionally  meet 
is  that  which  forms  part  of  a  more  or  less  complete  paralysis 
of  the  third  pair.  It  is  usually  accompanied  by  mydriasis  and 
frequently  by  paralysis  of  external  muscles.  It  seems,  however, 
that  it  may  exist  without  any  complication. — In  glaucoma  and 
cyclitis,  the  diminution  of  the  ampiltude  of  accommodation  is 
frequently  one  of  the  first  symptoms. 

SPASM  OF  ACCOMMODATION. — There  have  been  described  two 
forms  of  spasm  of  accommodation.  i°  As  we  have  seen,  one 
has  been  accustomed  to  diagnose  spasm  of  accommodation  when 
one  found  a  weaker  refraction  after  the  instillation  of  atropine. 
The  existence  of  this  supposed  spasm,  which  is  always  of  a 
very  low  degree  (0.50  to  1.50  D.),  is  very  doubtful,  since  the 
diminution  of  refraction,  after  the  instillation  of  atropine,  may 
often  be  attributed  to  the  weaker  refraction  of  the  peripheral 
parts  of  the  optic  system  of  the  eye. 

2°  We  sometimes  observe  in  hysterical  patients  a  true  spasm 
of  accommodation,  extending  most  frequently  to  the  entire 
amplitude,  and  not  to  a  small  part,  as  in  the  preceding  case. 


ACCOMMODATION  195 

These  cases  are  rare ;  they  give  rise  to  a  transient  myopia,  which 
is  generally  complicated  by  monocular  diplopia. 

84.  Mechanism  of  the  Accommodation.  Historical,  A. — Theor- 
etically, the  eye  could  accommodate  itself  by  one  of  the  follow- 
ing mechanisms: 

a.  INCREASE  OF  CURVATURE  OF  THE  CORNEA. 

b.  INCREASE  OF  CURVATURE  OF  THE  CRYSTALLINE  LENS. 

c.  ELONGATION  OF  THE  GLOBE. 

These  three  hypotheses  have  found  their  adherents,  as  also 
have  the  two  following  which  are  theoretically  impossible: 

d.  ADVANCE  OF  THE  CRYSTALLINE  LENS. 

e.  CONTRACTION  OF  THE  PUPIL. 

As  to  the  hypothesis  d,  we  must  note  that,  even  if  the  crystal- 
line lens  would  advance  so  as  to  touch  the  cornea,  this  advance 
would  not  suffice  to  explain  any  considerable  amplitude  of  ac- 
commodation.— The  accommodative  contration  of  the  pupil  was 
discovered  by  Schemer.  By  looking  through  an  opening  a  little 
smaller  than  the  pupil,  it  is  easy  to  convince  one's  self  that  this 
contraction  is  not  sufficient  to  explain  accommodation. 

Apart  from  these  five  theories,  there  have  been  proposed  still 
others,  much  less  plausible.  Kepler,  who  was  the  first  to  pro- 
pound the  problem  of  the  mechanism  of  accommodation,  sup- 
posed an  advance  of  the  crystalline  lens,  whilst  Descartes  was 
the  first  to  suppose  an  increase  of  curvature  of  this  organ. 

The  theory  of  the  change  of  curvature  of  the  cornea  found 
support  in  the  measurements  of  this  curvature  made  by  Home 
and  Ramsden  towards  the  end  of  the  last  century. — The  discus- 
sion continued  until  towards  the  middle  of  the  century,  and  the 
false  hypotheses  on  the  nature  of  accommodation  have  even 
resulted  in  two  beautiful  discoveries.  The  theoretical  researches 
of  Sturm  on  the  form  of  the  astigmatic  pencil  were,  indeed, 
undertaken  to  prove  that  accommodation  did  not  exist:  this 
author  thought  that  distant  objects  were  seen  with  the  posterior 


196 


PHYSIOLOGIC  OPTICS 


part  and  near  objects  with  the  anterior  part  of  the  focal  in- 
terval. On  the  other  hand,  when  Arlt  discovered  that  myopia 
depended  on  the  elongation  of  the  globe,  he  was  guided  by  a 
false  idea  on  accommodation.  He  thought  that  the  action  of 
the  external  muscles  produced  an  elongation  of  the  globe,  when 
one  is  forced  to  see  close  at  hand;  and,  as  it  was  known  that 
myopia  was  a  consequence  of  near  work,  he  concluded  that 
myopia  must  be  produced  by  an  elongation  of  the  globe.  On 
making  an  autopsy  on  some  excessively  myopic  eyes,  he  proved 
the  lengthening  of  the  globe  in  these  cases,  and  believed  that 
he  had  thus  confirmed  his  hypothesis.  We  now  know  that  this 
form  of  myopia  does  not  depend  on  near  work,  and  that  ac- 
commodation is  not  obtained  by  an  elongation  of  the  globe,  but 
by  an  increase  of  curvature  of  the  crystalline  lens! 

The  question  was  decided  by  the  observation  of  the  changes 
of  the  images  of  Pur kin je  during  accommodation,  which  prove 
that  accommodation  is  effected  by  an  increase  of  curvature  of 


Fig.  107. — Centripetal  movement  of  the  catoptric  image  of  the  anterior 
surface  of  the  crystalline  lens  during  accommodation.  (Discovered 
by  Cramer.) 


the  anterior  surface  of  the  crystalline  lens.  The  discovery  was 
made  in  1849  by  Max  Langenbeck,  but  attracted  scarcely  any 
attention;  it  was  only  after  the  beautiful  researches  of  Cramer 
(1851-52)  that  the  truth  was  definitely  accepted.  Cramer  con- 


ACCOMMODATION  197 

structed  an  instrument  which  he  called  ophthalmoscope,  with 
which  he  could  conveniently  observe  the  catoptric  images  of  the 
crystalline  lens,  and  it  was  easy  for  him  to  show  that  that  of 
the  anterior  surface  made,  during  accommodation.,  a  quite  ex- 
tended centripetal  movement.  This  fact  has  been  verified  by  all 
those  who  have  examined  the  catoptric  images  during  accommo- 
dation; it  is  due  to  the  increase  of  curvature  of  the  anterior 
surface. 

Let  ABD  (fig.  107)  be  the  surface  in  a  state  of  repose  and 
C  its  center,  A1ED1  the  surface  in  a  state  of  accommodation 
and  Cj  its  center,  O  an  object  (a  lamp  placed  at  a  great  distance). 
To  find  the  position  of  the  image,  we  draw  OC  (OCj)  (suppos- 
ing that  these  are  the  apparent  surfaces  we  need  not  take  into 
account  the  corneal  refraction).  The  image  must  be  on  this 
straight  line,  at  an  equal  distance  between  the  surface  and  center, 
at  I  for  the  surface  in  repose,  at  II  for  the  surface  in  a  state 
of  accommodation.  The  observing  eye  sees  the  images  pro- 
jected in  the  pupillary  plane,  it  sees  I  at  i  and  11  at  i^ ;  it  sees 
the  image,  therefore,  make  a  centripetal  movement  during  ac- 
commodation. It  is  the  same,  whatever  may  be  the  position  of 
the  observing  eye;  there  is  only  one  point  where  it  does  not 
see  motion,  viz.,  when  it  is  on  the  prolongation  of  line  II l:  in 
this  case  the  two  images  I  and  II  overlap,  and  there  is  no  ap- 
parent displacement.  The  line  II l  passes  through  the  point  B, 
the  place  where  the  two  surfaces  touch.  This  point  B,  towards 
which  the  apparent  movement  of  the  image  takes  place,  whatever 
may  be  its  position  in  the  pupil,  is  usually  situated  a  little 
outside  the  center  of  the  latter;  generally  it  is  found  almost  on 
the  optic  axis  of  the  eye. — Recently,  Coronat  again  described 
the  centripetal  movement,  whence  he  erroneously  inferred  a 
see-saw  movement  of  the  crystalline  lens. 

The  question  of  knowing  by  what  change  the  eye  accommo- 
dates itself  for  near  vision  being  solved,  it  remained  to  be  dis- 
covered by  what  means  the  change  was  effected.  Cramer  attri- 
buted the  change  to  the  contraction  of  the  iris;  he  thought  that 
the  iris  in  the  state  of  repose  was  greatly  swollen  in  front,  and 


198  PHYSIOLOGIC  OPTICS 

became  flattened  during  accommodation  by  a  simultaneous  con- 
traction of  the  sphincter  and  dilatator.  He  thought  that  it  thus 
exerted  a  pressure  on  the  peripheral  parts  of  the  crystalline 
lens,  and  that  the  ciliary  muscle,  contracting  at  the  same  time, 
exerted  a  traction  on  the  choroid,  which  pushed  the  vitreous 
body  forward.  In  this  way  the  crystalline  lens,  subjected  to  a 
pressure  in  its  whole  extent,  except  on  the  pupillary  part,  be- 
came swollen  at  this  place.  Several  other  theories,  conceived 
after  that  of  Cramer,  also  involved  the  participation  of  the  iris 
in  the  act  of  accommodation;  they  were  necessarily  abandoned 
when  Graefe  published  his  celebrated  case  of  complete  aniridia, 
of  traumatic  origin,  in  which  the  amplitude  of  accommodation 
was  intact. 

A  short  time  after  the  discovery  of  Cramer,  and  without  be- 
ing acquainted  with  his  work,  which  was  published  only  in 
the  Dutch  language,  Helmholtz  made  the  same  observation.  He 
used  as  his  object  the  distance  between  two  lamps  (or  a  lamp 
and  its  image  formed  by  a  mirror).  During  accommodation, 
the  distance  between  the  two  images  diminished  considerably, 
which  is  easy  to  understand,  since  a  sphere  forms  an  image 
smaller  in  proportion  as  its  radius  is  less. 

Helmholtz  confirmed,  moreover,  the  observation  made  pre- 
viously by  Hueck,  according  to  which  the  anterior  surface  of 
the  crystalline  lens  advances  a  little  during  accommodation.  He 
measured  the  thickness  of  the  crystalline  lens,  which  he  found 
a  little  greater  during  accommodation  than  in  a  state  of  repose. 
He  also  measured  two  dead  crystalline  lenses,  and  found  their 
thickness  greater  than  that  of  the  living  crystalline  lens  in  a 
state  of  repose.  He  further  concluded  that  there  was  a  slight 
increase  of  curvature  of  the  posterior  surface  of  the  crystalline 
lens  during  accommodation. 


ACCOMMODATION  199 

The  following  are  the  numbers  which  he  adopted  for  his 
schematic  eye,  compared  with  those  which  he  found  for  the 
dead  eye: 

SCHEMATIC   EYE  DEAD   EYE 

Eadius  of  the  anterior  surface..   10mm           6mm  10.16mm  8.87mm 

—        —        posterior    surface.     6mm           5.5mm        5.86mm  5.89mm 

Thickness     3.6mm         4mm  4.2mm  4.31mm 

Focal  distance    43.71mm  33.79mm  45.14mm  47.44mm 

Total   index    1.4545  1.4519         1.4414 

Later,  he  supposed  for  the  schematic  eye  an  index  of  14371, 
whichi  would  give  for  the  living  eye  in  repose  a  focal  distance 
of  50.62  mm.  and  for  the  eye  in  accommodation  39.07  mm. 

To  explain  the  mechanism  of  accommodation  Helmholtz  an- 
nounced the  following  hypothesis,  which  he  gave,  however,  only 
as  probable:  in  a  state  of  repose  the  crystalline  lens  is  kept 
flattened  by  a  traction  exerted  by  the  zonula.  When  the  ciliary 
muscle,  of  which  he  considered  the  anterior  extremity  as  fixed, 
contracts,  it  draws  the  choroid  slightly  forward,  which  relaxes 
the  zonula.  Having  become  free,  the  crystalline  lens  then 
swells  by  its  own  elasticity,  approaching  the  spherical  form. 

This  hypothesis  does  not  seem  to  have  been  at  first  generally 
accepted,  (i)  Hencke,  and  other  authors,  tried  to  explain  the 
phenomena  observed  by  other  hypotheses.  After  having  dis- 
covered the  supposed  circular  fibres  of  the  ciliary  muscle,  H. 
Muller  thought  that  this  muscle  changed  the  form  of  the  crys- 
talline lens  by  a  direct  pressure,  an  idea  which  was  abandoned 
when  it  became  known  that  the  ciliary  body  never  touches  the 
crystalline  lens. 

On  the  other  hand,  the  hypothesis  of  Helmholiz  was  strength- 
ened by  the  experiments  which  Hensen  and  Vaetkers  performed 
on  dogs.  They  thrust  very  fine  needles  into  the  eye  a  little 
behind  the  ora  serrata;  on  stimulating  by  the  electric  current 
the  ciliary  ganglion,  they  saw  the  free  extremity  of  the  needle 
describe  a  movement  backwards,  which  proves  that  the  choroid 


(1)  See  Donders.     Anomalies  of  the  Refraction  of  the  Eye.     London,  1864. 


200  PHYSIOLOGIC  OPTICS 

is  drawn  forwards.  The  phosphene  of  Czermak,  which  had 
also  been  seen  by  Purkinje,  also  indicates  a  traction  forwards 
of  the  interior  membranes  of  the  eye.  By  examining  eyes  on 
which  an  iridectomy  had  been  performed,  Coccius  also  estab- 
lished during  accommodation,  phenomena  which  could  militate 
in  favor  of  the  hypothesis  of  Helmholtz  (swelling  of  the  ciliary 
processes,  at  least  apparent  diminution  of  the  diameter  of  the 
crystalline  lens,  and  an  increase  in  the  width  of  its  border,  that 
is  to  say,  of  the  very  peripheral  part  which  is  seen  black  with 
the  ophthalmoscope). 

Thanks  to  these  observations,  thanks  also  to  the  ever  in- 
creasing fame  of  Helmholtz,  his  theory  ceased  little  by  little  to 
be  disputed,  and  his  followers,  more  loyal  than  the  king,  pro- 
claimed as  certain  what  he  had  himself,  with  much  reserve  ex- 
plained as  probable.  (2)  Thus,  Mauthner  declared  the  question 
of  accommodation  definitely  solved  by  the  theory  of  Helmholtz. 

Before  explaining  the  mechanism  of  accommodation  as  I 
intend  to,  I  must  add  some  remarks  to  the  historical  explanation 
which  we  have  just  read,  and  which  is  classical,  because  there 
have  been  authors  who  have  expressed  ideas  on  accommodation 
in  my  opinion  more  correct  than  those  in  vogue  up  to  the 
present  time.  First,  I  will  make  an  objection.  If  it  is  true  that 
the  crystalline  lens,  in  repose,  is  kept  flattened  by  a  traction 
exerted  by  the  zonula,  we  should  expect  to  find  the  dead  crys- 
talline lens,  taken  from  the  eye  in  its  capsule,  in  a  state  of 
maximum  accommodation,  or  perhaps  even  still  more  swollen, 
since  it  is  no  longer  exposed  to  any  traction.  The  followers 
of  Helmholtz  have,  indeed,  strongly  insisted  on  the  fact  that 

(2)  Great  men  are,  indeed,  too  reserved  through  fear  of  their  followers.  Helm- 
holtz formed  the  idea  of  comparing  the  cornea  to  an  ellipsoid,  and  although  he 
said  intentionally  that  the  cornea  does  not  resemble  such  a  surface,  this  idea 
has  so  taken  root  that  it  will  be  difficult  to  eradicate  it.  It  is  so  also  with  his 
ideas  of  accommodation  ;  if  we  take  the  trouble  to  compare  the  cautious  terms 
which  he  used,  with  the  mode  of  expression  of  his  followers,  we  shall  see  the 
difference.  The  participation  of  the  posterior  surface  of  the  crystalline  lens  in 
accommodation,  which  everybody  considers  as  certain,  had  for  Helmholtz  merely 
the  character  of  a  grand  probability. — Measuring  his  three  living  eyes,  he  found 
for  the  crystalline  lens  a  thickness  about  %mm.  less  than  that  of  dead  crystalline 
lenses ;  and  he  added :  "On  the  other  hand,  it  seems  to  me  very  improbable  that 
I  have  committed  an  error  of  a  %mm.  making  these  measurements."  In  the 
modern  treatises  we  read,  on  the  contrary:  "If  we  remove  the  crystalline  lens 
of  the  eye  of  a  young  person,  we  see  it  immediately  assume  a  spherical  form,"  etc. 


ACCOMMODATION  201 

he  found  the  dead  crystalline  lens  thicker  than  the  living  crys- 
talline lens  in  repose,  although  the  difference  does  not  seem  to 
exceed  the  limit  of  error  (see  page  85);  but,  if  we  take  the 
trouble  of  examining  his  numbers  (page  199),  we  shall  see 
that  his  dead  crystalline  lenses  were  by  no  means  in  a  state  of 
accommodation.  He  measured  in  all  three  living  eyes  and  found, 
as  radii  of  the  anterior  surface  of  the  crystalline  lens  in  repose, 
11.9  mm.,  8.8  mm.  and  10.4  mm.,  while  for  the  dead  eyes  he 
found  10.16  mm.  and  8.87  mm.  His  autopsies,  therefore,  by 
no  means  tell  in  favor  of  his  hypothesis. 

It  is  so  also  in  the  case  of  the  measurements  which  Stadfeldt 
undertook  recently.  He  measured  eleven  living  human  crystal- 
line lenses  in  a  state  of  repose,  with  the  ophthalmometer ;  the 
radius  of  curvature  of  the  anterior  surface  of  the  crystalline 
was  on  an  average  10.6  mm.,  while  the  average  of  the  same 
radius  of  the  six  dead  crystalline  lenses,  taken  from  the  eye 
in  the  capsule  and  measured  with  the  ophthalmometer  of  Javal, 
without  being  exposed  to  any  traction,  was  11.4  mm. 

85.  Mechanism   of   Accommodation.      Historical,   B. — It   was 

Young  who  first  demonstrated  that  accommodation  was  effected 
by  an  increase  of  curvature  of  the  crystalline  surfaces.  More- 
over, he  had  more  exact  ideas  on  what  happened  during  accom- 
modation than  those  which  are  actually  now  in  vogue.  He 
wrote  his  celebrated  treatise  on  the  mechanism  of  the  eye  in 
1 80 1,  and  it  is  truly  astonishing  that  nearly  a  century  should 
have  passed  before  his  book  was  understood  and  before  we 
came  to  know  as  much  as  he.  Before  proving  that  the  accom- 
modation is  effected  by  an  increase  of  curvature  of  the  crystalline 
lens,  he  begins  by  showing  that  there  can  be  question  only  about 
an  increase  of  curvature,  either  of  the  cornea  or  of  the  crystal- 
lin  lens,  or  of  a  lengthening  of  the  globe,  and  he  eliminates,  as 
theoretically  impossible,  the  other  hypotheses  which  had  been 
proposed. — Let  us  now  pass  to  his  analysis. 

a.  ACCOMMODATION  is  NOT  EFFECTED  BY  AN  INCREASE  OF 
CURVATURE  OF  THE  CORNEA. — Young  proved  this  thesis  by  a 


202 


PHYSIOLOGIC  OPTICS 


series  of  experiments,  several  of  which  closely  approach  our 
modern  ophthalmometric  methods.  Observing  the  corneal 
image  he  did  not  discover  the  least  change  during  accommoda- 
tion ;  he  obtained,  however,  a  very  visible  change  by  exerting  a 
pressure  on  a  peripheral  part  of  the  cornea,  and  this  change  of 
curvature  is  much  less  considerable  than  that  which  would  be 
necessary  to  explain  accommodation. 

It  is  evident  that  a  change  of  the  cornea  sufficient  to  explain 
accommodation  would  have  been  very  visible.  Young,  who  ex- 
perimented with  his  own  eyes,  was  at  this  time  27  years  old, 
and  his  amplitude  of  accommodation  measured  about  10  D. 
Actually,  we  can  easily  measure  a  quarter  of  a  dioptry. 

His  most  conclusive  experiment  consisted  in  putting  the  eye 
under  water  (fig.  108)  :  he  took  a  weak  objective  of  a  micro- 
scope which  had  very  nearly  the  same 
refraction  as  the  cornea,  filled  the 
tube  with  water,  and  placed  it  before 
his  eye  also  plunged  into  water.  In 
these  conditions,  the  action  of  the 
cornea,  which  was  surrounded  by  the 
liquid  on  both  sides,  was  eliminated 
and  replaced  by  that  of  the  objective. 
Now  in  this  experiment  the  ampli- 
tude of  the  accommodation  remained 
Fig.  108. — Method  of  putting  intact 

the  eye  under  water.     (Af-       ,  ,-, 

ter    Young  )  ^      ACCOMMODATION      IS     NOT     EF- 

FECTED BY  AN   ELONGATION   OF  THE 

GLOBE. — To  prove  this  fact  Young  employed  a  method  which 
he  could  use  because  he  had  very  prominent  eyes.  He  turned 
the  eye  inwards  as  much  as  he  could,  and  applied  against  its 
anterior  surface  a  strong  iron  ring;  then  he  thrust  the  ring  of 
a  little  key  on  the  external  side  between  the  eye  and  the  bone, 
until  the  phosphene  reached  the  fovea.  The  rings  were  kept 
at  a  fixed  distance.  Placed  between  the  iron  ring  and  that  of 
the  key,  the  eye  could  not  lengthen.  He  should  therefore,  if 


ACCOMMODATION  203 

accommodation  was  effected  by  a  lengthening  of  the  globe,  either 
find  it  abolished,  or  see  in  every  case  the  phosphene,  due  to 
the  pressure,  extend  over  a  much  greater  surface.  But  in  these 
conditions  the  accommodation  remained  unaltered,  and  the  width 
of  the  phosphene  did  not  change. 

c.  PERSONS   OPERATED   ON    FOR   CATARACT   HAVE   LOST   ALL 
TRACE  OF  ACCOMMODATION. — By  measuring  with  his  optometer 
persons  operated   on   for  cataract,    Young  easily  succeeded  in 
proving  this  fact. 

d.  He  then  explained  the  direct  proofs   of  the  increase  of 
curvature  of  the  crystalline  lens.     It  was  to  these  experiments 
that  I  alluded  when  I  said  that  he  had,  on  accommodation,  ideas 
which  are  ahead  of  our  own  time.     I  again  performed  these 
experiments  some  years  ago,  and  it  was  by  starting  from  them, 
by   repeating  them   and   adding   others   to  them,   that    on,  the 
mechanism  of  accommodation  I  have  come  to  form  ideas  which 
differ  materially   from  those  which  have   been  current  up  to 
the  present. 

It  was  impossible  for  Young  to  describe  clearly  the  mechanism 
of  accommodation,  because  at  that  time  the  non-striped  muscle 
fibres  were  unknown,  which  kept  him  from  suspecting  the  con- 
tractility of  the  body  known  later  as  the  ciliary  muscle;  he  was 
thus  led  to  postulate  the  contractility  of  the  crystalline  lens, 
an  hypothesis  which  he  soon  abandoned.  His  researches  in  this 
direction  necessarily  could  not  but  remain  fruitless. 

The  ciliary  muscle  was  discovered,  at  the  same  time  and 
separately,  by  Bowman  and  Bruecke  (in  1846).  Ideas  on  the 
structure  and  function  of  this  muscle  have  varied  considerably. 
Sometimes  the  anterior  extremity,  sometimes  the  posterior  ex- 
tremity has  been  considered  as  fixed;  sometimes  the  mobility 
of  both  extremities  was  taken  for  granted  (Bonders),  sometimes 
both  were  considered  fixed.  The  oldest  descriptions  seem  to  be 
the  best,  especially  that  of  H.  Muller;  most  of  the  modern 
works  seem  influenced  by  the  hypothesis  of  Helmholtz.  Ac- 


204 


PHYSIOLOGIC  OPTICS 


cording  to  H.  Muller,  we  must  distinguish  between  a  longer 

superficial  part  (fig.  109) 
composed  of  longitudinal 
fibres  which  are  inserted  in 
front  on  the  sclera,  near 
the  canal  of  Schlemm,  and 
which  are  lost  behind  in 
the  choroid,  and  a  deep 
part,  also  composed  in 
greater  part  of  longitud- 
inal, but  shorter,  fibres,  and 
not  going  so  far  either  in 
front  or  behind,  as  the 
superficial  fibres.  These 
fibres  are  not  inserted  in 
the  sclera.  The  deepest 
layer  is  composed  of 
oblique  or  even  circular 
fibres.  Muller  thought  that 
)they  formed  a  true  sphincter,  but  the  existence  of  such  a 
sphincter  is  by  no  means  proved;  after  holding  for  some  time 
a  circular  direction,  these  fibres  seem  to  change  their  course 
and  to  continue  in  the  deep  longitudinal  fibres.  It  seems  that 
at  least  a  part  of  the  deep  longitudinal  fibres  ends  thus ;  others 
seem  to  end  free,  without  insertion,  in  the  part  of  the  muscle 
which  goes  towards  the  anterior  chamber. 

By  dividing  a  hardened  eye  into  two  halves  by  a  longitudinal 
section,  we  easily  discover  the  small  white  triangle  of  the  ciliary 
muscle.  If  we  then  exert  a  traction  upon  the  iris  in  order  to 
separate  the  ciliary  body  from  the  sclera,  we  do  not  tear  the 
muscle  from  its  insertion  near  the  canal  of  Schlemm,  but  we 
divide  it  into  two  leaflets,  both  of  which  end,  behind,  in  the 
choroid.  In  the  fresh  eye  there  also  always  remains  a  part 
of  the  muscle  adhering  to  the  sclera  as  Mannhardt  had  already 
observed.  When  making  this  experiment  we  produce  an  appear- 
ance which  forcibly  recalls  the  ciliary  muscle  of  certain  animals 


Fig.  109. — Ciliary  muscle  of  man. 
(After  H.  Muller.') 

a,  cornea;  6,  sclera;  c,  iris;  d,  ciliary 
process;  e,  canal  of  Schlemm;  /, 
longitudinal  fibres;  g,  circular 
fibres;  h,  transitional  fibres  of  the 
ciliary  muscle. 


ACCOMMODA  TION 


205 


(the  cat,  for  example,  fig.  no),  in  which  the  muscle  is  divided 

in     front     into     two 

parts  separated  by  a 

prolongation    back- 

wards    of    the    space 

of  Fontana. 

Among  the  authors 
who  have  reached  a 
result  different  from 
that  of  Helmholts,  I 
shall  mention  Mann- 
hardt,  who,  by  a 
study  of  the  compara- 
tive anatomy  of  the 
ciliary  muscle,  reach- 
ed the  conclusion  that 
it  is  the  posterior  ex- 
tremity of  the  muscle 
which  should  be  con- 
sidered as  fixed,  and  FiS-  HO.— Ciliary  part  of  the  eye  of  a  cat. 
,  ,  ,  , .  a,  Ciliary  muscle  dividing  in  front  into 

that  accommodation        two  leaflets.  6>  canal  of  Fontana.  c>  cornea 

must  be  produced  by        a,  iris. 

a  traction  exerted  by  the  ciliary  muscle  on  the  zonula.  He  was 
vigorously  attacked  by  H.  Miiller,  and  his  work  scarcely  at- 
tracted attention  because  it  could  not  be  considered  that  a  traction 
on  the  zonula  could  produce  an  increase  of  the  curvature  of  the 
crystalline  surfaces.  We  cite,  moreover,  the  remarkable  obser- 
vations of  Foerster  (1864),  according  to  which  the  tension 
diminishes  in  the  anterior  chamber  during  accommodation.  He 
observed  several  patients  in  whom  he  performed  paracentesis 
so  that  the  iris  and  crystalline  lens  were  nearly  in  contact  with 
the  cornea.  When  the  patient  made  an  effort  of  accommodation, 
the  middle  of  the  cornea  became  depressed  to  assume  its  old 
form  by  the  relaxation  of  the  accommodation.  It  must  be  noted, 
however,  that  the  phenomenon  persisted  after  instillation  of 
atropine.  In  persons  having  a  corneal  fistula  he  obtained  an 


206  PHYSIOLOGIC  OPTICS 

almost  immediate  effect  from  atropine  by  placing  a  drop  in  the 
conjunctival  sac  and  making  an  effort  of  accommodation,  the 
liquid  being  sucked  into  the  anterior  chamber  by  the  diminution 
of  tension.  These  beautiful  observations,  which  Arlt  declared 
equivalent  to  physiologic  experiments,  are  scarcely  explicable 
by  the  theory  of  Helmholtz. 

86.  Personal  Experiments. — Finally  I  come  to  my  own  experi- 
ments on  accommodation:  the  first  (i°)  are  derived  from  the 
statements  of  Young. 

i°  The  amplitude  of  accommodation  diminishes  towards  the 
periphery  of  the  pupil. 

a.  ABERROSCOPIC  PHENOMENA. — We  have  already  seen  that 
with  the  aberroscope  (see  page  122)  most  persons  see  the 


I  .;        .^       II 

Fig.  111. — Change  of  aberroscopic  phenomena  during  accommodation. 
I,  Repose.    II,  Accommodation. 

shadows  concave  towards  the  periphery.  But,  on  making  an 
effort  of  accommodation,  the  form  of  the  shadows  change :  they 
turn  their  concavity  towards  the  middle,  which  indicates  that  the 
refraction  increases  towards  the  middle  (fig.  in).  After  what 
we  have  said  on  page  118  it  follows  that  the  central  refraction 
must  have  increased  more  than  the  peripheral  refraction. 

Some  people  in  a  state  of  repose  see  shadows   straight  or 
slightly  concave  towards  the  middle.     In  such  people  this  de- 


ACCOMMODATION  207 

formity  becomes  still  more  pronounced  during  accommodation. 
b.  CHANGE  OF  THE  CIRCLE  OF  DIFFUSION. — If  we  observe  a 
distant  luminous  point,  after  having  made  the  eye  myopic,  it 
appears  under  the  form  of  a  luminous  disc,  the  brightness  of 
which  is  generally  uniform  or  concentrated  at  the  middle.  Dur- 
ing accommodation  we  see  it  change  its  appearance;  we  see  a 
feebly  luminous  disc  surrounded  by  a  bright  border.  According 
to  the  explanation  given  on  page  117,  this  observation  means, 
like  the  preceding  one,  that  the  spherical  aberration  is  over- 
corrected  during  accommodation,  that  is  to  say,  that  the  central 
accommodation  is  greater  than  the  peripheral  accommodation. 
Although  accommodation  may  increase  the  refraction  of  the  eye 
by  many  dioptrics,  the  circle  of  diffusion  increases  only  slightly, 


Fig.  112. — Appearance  of  the  luminous  point  (right  eye  of  Professor 
Roster,  treated  with  cocaine). 

at  least  when  the  pupil  is  dilated.  Figure  112.  shows  the  ap- 
pearance of  the  circle  of  diffusion  of  an  emmetropic  eye;  ren- 
dered 8  D.  myopic  by  a  convex  lens,  this  eye  sees  the  circle  of 
diffusion  represented  by  a,  figure  113,  while  b,  same  figure,  repre- 
sents the  form  under  which  it  sees  a  luminous  point  by  making 
an  effort  of  accommodation  of  8  D.  without  a  lens.  The  pupil 


208  PHYSIOLOGIC  OPTICS 

was  dilated.  The  explanation  of  the  phenomenon  is  easy:  let 
us  imagine  the  pupil  and  circle  of  diffusion  divided  into  cor- 
responding zones;  it  is  clear  that  if  the  accommodation  is  every- 
where the  same,  all  the  zones  of  the  diffusion  circle  ought  to 
increase,  while,  if  the  accommodation  diminishes  towards  the 
periphery,  the  outside  zones  increase  little  or  nothing  and  the 
central  zones,  on  increasing,  come  to  partly  cover  the  peripheral 


a  ~b 

Fig.  113. — The  same  eye  as  in  figure  112. 

a,  Appearance  of  the  luminous  point,  the  eye  being  rendered  myopic  8  D. 
with  a  convex  lens  (Eepose).  b,  Appearance  of  the  luminous  point, 
without  lens,  the  eye  accommodating  8  D. 

Measured  with  the  optometer  of  Yowig,  the  central  accommodation  was 
8  D. ;  the  peripheral  accommodation  (at  2.5mni  from  the  axis)  was 
3.3  D. 

zones.  This  is  the  reason  why  the  circle  of  diffusion  is  sur- 
rounded during  accommodation  with  a  bright  border,  without 
increasing  much  in  diameter. 

c.  MEASUREMENT  WITH  THE  OPTOMETER  OF  YOUNG. — The 
optometer  of  Young  enables  us  to  measure  directly  the  differ- 
ence betwen  the  central  accommodation  and  peripheral  accom- 
modation. 


ACCOMMODATION  209 

We  measure  the  central  accommodation  with  the  two  nearest 
slits  (see  page  122),  which  we  place  as  nearly  as  possible  at  the 
middle  of  the  pupil,  and  the  peripheral  accommodation  with  the 
triangular  plate  which  we  lower  just  enough  to  be  able  to  see 
see  the  two  lines.  In  this  way  we  prove  that  at  the  border  of  the 
pupil  (supposed  to  be  five  millimeters)  the  amplitude  of  the 
accommodation  is  only  half  the  central  accommodation  or  still 
less.  If,  after  having  dilated  my  pupil  to  the  utmost  (with  a 
mixture  of  cocaine  and  homatropine) ,  I  use  an  interval  of  7 
millimeters,  my  accommodation  which,  at  the  middle  of  the 
pupil,  is  2.5  D.  to  3  D.,  diminishes  nearly  to  zero  (0.2  D.)  on 
the  borders.  Here  are  some  measurements: 

Central  amplitude    Peripheral  amplitude 
( interval  0.75  mm, ) .     ( interval  5  mm. ) . 

Young    9.8  D.  4.2     D. 

Koster    8      D.  3.3     D. 

Demicheri    7.5  D.  3.7     D. 

6     D.(l)  3       D. 

4     D.(l)  2        D. 

Mme    T 6.7  D.  3.8     D. 

Tscherning    3      D.  1.25  D. 

We  find  still  more  considerable  differences  between  the  central 
and  peripheral  accommodation,  by  placing  the  two  slits  sometimes 
at  the  middle  of  the  pupil,  sometimes  near  the  borders : 

AMPLITUDE    OF    ACCOMMODATION 

Temporal  border.  Center.  Nasal  border. 

Demicheri    (Homatropine)     6      D.       2  D 

0  4      D.(1)I  D. 

Mme    T 5        D.     6.7  D.      5  D. 

Tscherning   (Homatropine)    0.25  D.     H      D.       0 

d.  SKIASCOPIC  EXAMINATION. — Observations  a  and  b  are  easy 
to  make,  but  they  require  that  the  observer  be  young,  that  his 
pupil  be  well  dilated  and  that  he  be  master  of  his  accommoda- 
tion ;  observations  with  the  optometer  of  Young,  as  well  as  those 
with  the  ophthalmometer,  which  I  shall  describe  forthwith,  are 
quite  delicate  and  require  special  instruments.  But  we  possess 


210  PHYSIOLOGIC  OPTICS 

in  skiascopy  with  a  luminous  point  a  very  convenient  means  of 
studying  the  nature  of  accommodation.  To  make  the  observation 
we  select  a  child  or  a  young  person  whose  pupil  is  well  dilated 
with  cocaine.  It  is  better  to  select  a  person  whose  pupil  is  well 
dilated,  who  is  almost  emmetropic,  and  who  has  not  too  much 
aberration  in  a  state  of  repose.  We  place  the  lamp,  surrounded 
with  its  perforated  screen,  at  one  side  of  and  a  little  behind 
the  observed  person  and  we  project  light  on  his  eye  by  means  of  a 
concave  mirror,  which  forms  the  image  of  the  opening  at  15  to 
20  cm.  from  the  observed  eye,  in  which  position  we  place  a 
mark  of  fixation.  As  long  as  the  observed  person  does  not 
accommodate,  the  condition  of  Jackson  is  not  fulfilled,  and  we 
see  the  pupil  entirely  illuminated,,  but  at  the  moment  when  the 
observed  person  fixes  the  fixation  mark  the  ring  of  over-corrected 
aberration  appears  with  all  desirable  distinctness.  The  phe- 
nomena is  especially  striking  if  we  compare  the  appearance  of 
the  accommodated  eye  with  that  of  the  non-accommodated  eye, 


Fig.  113a. — STciascopic  examination  of  accommodation,  a,  Appearance  of 
the  emmetropic  eye  made  myopic  with  a  lens  of  -|-5  D.  &,  Appear- 
ance of  the  same  eye,  accommodating  5  D.  without  lens. 

made  myopic  with  a  convex  glass  (fig.  1130).  We  have  observed 
(page  119)  that  we  see  luminous,  under  these  circumstances,  the 
parts  of  the  observed  pupil  which  send  light  into  the  observing 
eye.  Placed  at  50  cm.  the  existence  of  the  ring  indicates,  there- 
fore, that  there  are,  towards  the  borders  of  the  pupil,  parts,  the 
myopia  of  which  does  not  exceed  2  D.,  for  otherwise  the  rays 


ACCOMMODATION  211 

proceeding   from   these  parts   would  have  already  crossed  the 
axis,  and  would  not  enter  into  the  observing  eye.    To  determine 


fcs 

Fig.  114. — Reflection  images,  on  the  anterior  surface  of  the  crystalline  of 
my  right  eye,  of  three  lamps  placed  on  a  horizontal  line,  a,  in  a 
state  of  repose;  fci  62  6s,  in  different  stages  of  accommodation. 
Highest  accommodation  3  D.  with  cocaine. 


the  degree  of  aberration  produced  by  accommodation,  we  ap- 
proach nearer  and  nearer  the  point  of  fixation ;  the  ring  becomes 
thinner  and  thinner,  but  it  is  rare  that  it  disappears  completely 
before  the  accommodation  attains  a  very  high  degree.  I  have 
thus  shown  that  a  central  accommodation  of  8  D.  accompanied 
a  peripheral  accommodation  of  2  D.  in  a  case  in  which  the  pupil 
was  very  large.  The  condition  was,  therefore,  still  more  pro- 
nounced than  in  the  cases  which  I  examined  with  the  optometer. 
The  phenomena  may  present  themselves  a  little  differently  if 
the  positive  aberration  is  very  pronounced  in  a  state  of  repose, 
but  on  making  the  calculations  we  obtain  the  same  result. 

2°  During  accommodation  the  anterior  surface  of  the  crystal- 
line lens  increases  in  curvature  at  the  middle,  white  it  is  flattened 
towards  the  periphery. 

I  place  the  arc  of  the  ophthalmophakometer  horizontally,  and 
attach  three  incandescent  lamps  to  it,  so  that  they  are  on  the 
same  horizontal  line  and  just  far  enough  apart  for  all  three 
images  formed  by  the  anterior  surface  of  the  crystalline  lens 
to  be  visible  in  the  pupil.  I  direct  the  look  of  the  observed 
person  so  that  the  three  images  are  situated  near  the  upper 
border.  In  a  state  of  repose  they  are  arranged  in  a  straight  line 
(fig.  1140)  or  following  a  curve  slightly  concave  towards  the 
center  (fig.  115  A)  ;  during  accommodation,  they  form  a  curve 


212 


PHYSIOLOGIC  OPTICS 


convex  towards  the  middle  (fig.  114  blf  b2,  63,  115  B),  and  the 
curvature  of  which  is  more  pronounced  in  proportion  as  the 
accommodation  is  greater. 


Fig.  115. — Eeflection  images  of  the  right  eye  of  Mme  T. — A,  in  a  state  of 
repose;  B,  during  accommodation  (after  a  drawing  of  Professor 
Koster). — a,  corneal  images;  6,  images  of  anterior  surface  of  the 
crystalline  lens.  Accommodation  of  6  D. 

It  is  easy  to  see  that  this  phenomenon  indicates  a  greater 
curvature  at  the  middle  than  towards  the  periphery:  indeed,  let 
us  suppose  for  an  instant  that  we  have  added  three  other  lamps, 
which  would  form  their  images  near  the  lower  border  of  the 
pupil,  and  let  us  consider  as  objects  the  distances  between  the  two 
lamps  situated  on  the  same  vertical  line.  We  would  thus  have 


Repose 


Accommodation 


Fig.  116. 


three  equal  objects,  the  images  of  which  would  be  of  the  same 
size  in  a  state  of  repose  (aa,  fig.  116),  which  indicates  that  the 
curvature  is  the  same  everywhere;  but,  during  accommodation, 
the  image  (b,  fig.  116)  of  the  middle  is  considerably  smaller 


ACCOMMODATION 


213 


than  the  other  two,  b1  b1}  which  indicates  that  the  curvature  is 
greater  at  this  place. 

We  observe  an  analogous  phenomenon  on  the  cornea,  in  cases 
of  keratoconus.  The  keratoscope  of  De  Wecker  and  Masselon 
is  formed  by  a  white  square  on  a  black  ground.  On  examining 
a  case  of  keratoconus  with  this  instrument,  and  causing  the  look 
to  be  so  directed  that  the  apex  of  the  keratoconus  coincides  with 
the  axis  of  the  instrument,  we  see  the  sides  of  the  image  of  the 
square  assume  the  form  of  curves  turning  their  convexity  to- 
wards the  middle  (fig.  117). 

We  might  think,  from  these  phenomena,  that  the  curvature 
of  the  peripheral  parts  increases  during  accommodation,  but  less 


Fig.  117. — Deformity  of  the  corneal  image  of  a  white  square  m  a  case  of 
keratoconus.     (After  Masselon.') 

than  that  of  the  central  part.  Nothing  of  the  kind:  the  peri- 
pheral parts  undergo  a  real  flattening  which  causes,  however, 
an  increase  of  refraction.  To  understand  this  fact,  which  might 
appear  paradoxical,  we  must  recall  what  I  have  said  on  page  17 
on  refraction  by  surfaces  of  the  second  degree.  Outside  of  the 
axis,  it  is  the  normal  and  not  the  radius  of  curvature  which,  for 
refraction  (and  also  for  reflection),  plays  the  part  of  the  radius 
of  the  sphere,  supposing  that  the  luminous  point  (or,  in  the 
case  of  reflection,  the  observing  eye)  is  on  the  axis. 


214 


PHYSIOLOGIC  OPTICS 


In  figure  118,  BDE  represents  a  curve  of  the  second  degree, 
AF  its  axis,  BH  the  radius  of  curvature  at  the  point  B,  BG 
the  normal  at  this  point  and  the  dotted  curve  a  circle  drawn 
with  BG  as  radius.  The  luminous  ray  AB  is  refracted  in  the 
direction  BF,  exactly  as  if  the  surface  were  replaced  by  the 
circle  BE. 

The  measurements  which  we  have  made  with  the  optometer 
of  Young  enable  us  to  calculate  approximately  the  form  of  the 
surface,  and  the  calculation  will  explain  at  the  same  time  what 
I  have  just  said.  Let  us  suppose  that  all  the  accommodation  is 
effected  by  the  anterior  surface,  and  let  us  take  the  experiment 
of  Demicheri  as  an  example.  He  had,  at  the  middle,  an  accom- 


Fig.  118.  —  Bef  raction  by  a  parabolic  surface. 

modation  of  7.5  D.,  at  2.5  mm.  from  the  axis  an  accommodation 
of  3.7  D.  Let  us  suppose  10  millimeters  for  the  radius  of  the 
anterior  surface  in  a  state  of  repose  and  1.06  for  the  index  of 
the  crystalline  lens  in  relation  to  the  aqueous  humor.  We  express 
the  refraction  of  the  surface  by  the  inverse  of  the  anterior  focal 
distance  =JL=_=6  D.  During  accommodation  the  cen- 


tral refraction  increased  7.5  D.  ;  the  refraction  of  the  surface 
would  be,  therefore,  at  this  place  13.5  D.  Whence  we  obtain 
the  radius  po  by  the  formula  «  —  i^gjg^  13.5  D.,  which  gives 

po         ^/o 

/>o—  4.44.  At  2.5  mm.  from  the  axis  the  accommodation  was 
3.7  D.,  the  refraction  of  the  surface  in  a  state  of  accommodation 


ACCOMMODATION 


215 


6  D.  +3.7  D.=9.7  D.,  and  the  normal  N,  at  this  place,  would 
be  found  by  the  formula  M~l  =9.7=  OM  ,  which  gives  N=6.i 
mm.  We  can  then  find  the  radius  of  curvature  p,  at  this  place, 
by  the  formula  P=™,  which  holds  good  for  all  surfaces  of  the 
second  degree.  It  gives  p=i2  millimeters.  We  see  that  the 
surface  is  already  flattened  at  this  place  during  accommodation, 

and  it  is  manifestly  flattened 
still  more  farther  towards  the 
periphery.  If  a  small  part  of 
the  accommodation  is  effected  by 
the  posterior  surface,  as  is  prob- 
able, the  flattening  of  the  an- 
terior surface  towards  the  peri- 
phery must  be  still  greater,  for 
it  is  probable  that  the  part  of 
the  accommodation  which  is  due 
to  the  posterior  surface  dimin- 
ishes relatively  much  less  quickly 
towards  the  periphery.  Suppos- 
ing that  the  portion  of  the  ac- 
commodation due  to  the  poster- 
ior surface  be  i  D.,  as  well  at 
the  center  as  near  the  border  of 
the  pupil,  we  would  have  for 
the  anterior  surface  po=4.8 
mm.,  p=i4.2  mm.  The  surface 
would  have  the  form  of  a  quite 
flattened  hyperboloid  (fig.  119), 
the  apex  of  which  would  corre- 
spond very  nearly  with  the  optic 
axis  of  the  eye,  and  would  be 
found  a  little  outside  the  visual 
line.  It  is  interesting  to  observe 
that  among  all  the  surfaces  of 
the  second  degree  having  />o— 4.8  mm.,  it  is  this  hyperboloid 
which  most  nearly  approaches  the  form  of  the  surface  in  a  state 


Fig.  119. — Deformity  of  the  crys- 
talline surfaces  during  accommo- 
dation. The  full  curves  indicate 
the  shape  in  a  state  of  repose, 
the  dotted  curves  the  accommo- 
dative shape.  (Accommodation 
7  D.) 


216  PHYSIOLOGIC  OPTICS 

of  repose.    Accommodation  is  effected,  therefore,  by  a  minimum 
deformity. 

3°  By  placing  the  cursor  A  of  the  ophthalmophakometer 
above  the  telescope,  and  requesting  the  observed  person  to  look 
towards  the  latter,  we  observe,  when  he  makes  an  effort  of 
accommodation,  the  following  phenomena  (fig.  120)  : 

I.  The  image  of  the  anterior  surface  of  the  crystalline  descends 
quickly  towards  the  corneal  image,  and  is  finally  hidden  behind 
the  latter.     It  is  this  displacement  which  has  been  described  by 
Cramer.     Towards  the  end  of  this  phase  the  pupillary  contrac- 
tion begins. 

II.  This  movement  ended,  the  small  image  of  the  posterior 
surface  of  the  crystalline  descends  in  its  turn  by  a  slow  and 


A  B 

Fig.  120. — The  four  apparent  phases  of  accommodation.  •  Corneal  image. 
— O  Image  of  the  anterior  surface  of  the  crystalline. —  '  Image  of 
the  posterior  surface  of  the  crystalline.  A,  accommodation;  B, 
relaxation. 

abrupt  movement.  Its  displacement  is  much  less  than  that  of 
the  large  image;  and,  while  the  latter  moves  in  a  straight  line, 
the  small  image  is  displaced  in  a  curve  with  its  concavity  turned 
towards  the  middle.  The  pupillary  contraction  is  greatest  dur- 
ing this  phase. 

III.  When  the  observed  person  relaxes  his  accommodation,  the 
small  image  again  ascends  to  resume  its  old  place  with  a  quick 
movement,  as  if  moved  by  a  spring. 

IV.  This  movement  ended,  the  large  image  re-ascends  in  its 
turn ;  its  movement  is  rather  slow,  and  as  if  hesitating. 


ACCOMMODATION 


217 


The  accommodative  phenomena  seem,  therefore,  to  take  place 
in  two  steps. 

During  the  displacement  of  the  small  image,  the  large  one 
is  concealed  behind  the  corneal  image,  so  that  we  cannot  see 


-11 


Fig.  121. — Eight  eye  of  Mme  T. — Displacements  of  the  image  of  the 
posterior  surface  during  accommodation,  observed  with  the  ophthal- 
mophakometer.  C,  by  fixing  the  telescope;  D,  by  looking  to  the 
right;  G,  by  looking  to  the  left;  H,  by  looking  upwards;  B,  by 
looking  downwards. — The  large  white  spot  is  the  corneal  image,  the 
two  small  white  spots  indicate  the  position  of  the  image  of  the 
posterior  surface  of  the  crystalline  in  a  state  of  repose  and  during 
accommodation.  The  arrows  indicate  the  direction  of  the  displace- 
ment which  takes  place  when  an  effort  of  accommodation  is  made. 

whether  it  is  displaced  or  not;  it  is  not  easy  to  find  a  direction 
of  the  look  such  that  we  can  follow  the  two  crystalline  images 


218  PHYSIOLOGIC  OPTICS 

during  the  entire  accommodative  displacement.  Sometimes  they 
are  concealed  behind  the  corneal  image,  sometimes  behind  the 
iris.  I  have,  however,  succeeded  in  doing  so  by  using  two  lamps, 
one  for  each  image;  in  this  way,  we  can  satisfy  ourselves  that 
the  large  image  undergoes  a  slight  displacement  downwards  at 
the  same  time  as  the  small  one,  but  this  displacement  of  the 
large  image  is  concealed  by  the  corneal  image  when  we  perform 
the  experiment  as  I  have  just  described.  It  is  especially  easy  to 
observe  the  displacement  downwards  of  the  large  image,  if  the 
direction  of  the  look  of  the  observed  person  is  such  that  the 
image  in  repose  is  placed  near  the  internal  or  external  border 
of  the  pupil.  The  movement  of  Cramer  then  takes  place  in  a 
horizontal  direction.  Having  reached  the  end,  the  image  makes 
a  bend,  becoming  displaced  a  little  downwards,  but  this  latter 
displacement  is  much  less  than  that  of  the  small  image.  I 
may  add  that  the  small  image  is  displaced  downwards,  whatever 
may  be  its  position  in  the  pupil  (fig.  121),  which  indicates  that 
the  cause  can  be  sought  neither  in  the  increase  of  curvature  of 
the  surface,  nor  in  a  displacement  forwards  or  backwards  of  the 
crystalline  lens.  But  this  displacement  downwards  of  the  image 
is  combined  with  a  quite  small  centripetal  displacement,  which 
also  takes  place  whatever  may  be  the  position  of  the  image  in 
the  pupil,  and  which  is  probably  due  to  a  slight  recession  of  '.he 
posterior  surface. 

The  observation  has  again  been  made  by  Hess  and  Heine. 
They  have  found  that  the  displacement  of  the  small  image  takes 
place  downwards,  whatever  may  be  the  position  of  the  head;  if 
we  lean  the  head  on  the  right  shoulder,  the  displacement  of  the 
small  image  takes  place  towards  the  side  which  is  downwards, 
that  is  to  say,  for  the  right  eye  towards  the  temporal  border  of 
the  pupil,  for  the  left  eye  towards  the  nasal  border.  I  was  able 
to  verify  this  observation,  which  seems  to  indicate  that  the  change 
takes  place  under  the  influence  of  the  weight.  Hess  also  ob- 
served that  an  entoptic  figure,  situated  on  the  posterior  surface 
of  the  crystalline  lens,  is  displaced  downwards  by  a  maximum 
accommodation,  whatever  may  be  the  position  of  the  head. 

4°    Other   Phenomena   Accompanying   Accommodation. — We 


ACCOMMODATION  219 

have  seen  that  Hueck  discovered  a  slight  advancement  of  the  an- 
terior surface;  Helmholtz  confirmed  this  observation.  It  is 
possible  that  we  may  sometimes  meet  such  a  displacement,  al- 
though the  experiment  of  Helmholtz  did  not  succeed  very  well 
with  me,  and  although  I  am  not  sure  that  his  observations  do 
not  admit  of  another  explanation.  In  the  eye  with  which  I  have 
made  my  experiments,  the  anterior  surface  did  not  advance ;  the 
part  corresponding  to  the  pupil  did  not  change  its  place,  but 
the  part  covered  by  the  iris  receded  with  this  membrane.  There 
is  formed  during  accommodation,  at  the  anterior  surface  of 
the  iris,  a  circular  depression  (fig.  122),  the  peripheral  border 
of  which,  corresponding  to  the  ciliary  body,  rises  in  a  peak, 
while  the  central  border  presents  a  very  gentle  slope,  corre- 
sponding to  the  anterior  surface  of  the  crystalline  lens.  I 
commend  this  observation,  which  was  already  made  by  Cramer, 
but  which  has  often  been  regarded  as  proving  an  enlargement 
of  the  anterior  chamber  in  the  angle  of  the  iris;  it  is  easy  to 
see  that  the  most  peripheral  parts  of  the  posterior  partition  of 
the  anterior  chamber  do  not  recede.  The  phenomena  are  not 


b 

Fig.  122. — Change  of  the  anterior  chamber  during  accommodation; 
a,  repose;   b,  accommodation. 

always  equally  pronounced,  but  we  can  nearly  always  find  at 
least  a  trace  of  them  in  young  subjects.  We  can  make  the  ob- 
servation by  oblique  illumination,  but  the  use  of  the  magnifying 
glass  (monocular)  is  not  to  be  recommended;  binocular  vision  is 
necessary  in  order  to  properly  account  for  the  change  in  the 
level  of  the  iris.  When  the  phenomenon  is  quite  pronounced,  we 
thus  obtain  a  quite  distinct  idea  of  the  conical  form  which  the 
anterior  crystalline  assumes  during  accommodation. 

As  to  the  posterior  surface  of  the  crystalline  lens,  its  changes 
are  less  manifest.  We  have  seen  that  the  catoptric  phenomena 
seem  to  indicate  a  slight  increase  of  curvature.  The  posterior 
surface  remains  very  nearly  in  its  place  during  accommodation ; 


220  PHYSIOLOGIC  OPTICS 

sometimes,  however,  we  observe  phenomena  which  seem  to  in- 
dicate that  it  recedes  a  little. 

The  much-discussed  question  of  knowing  whether  the  thick- 
ness of  the  crystalline  lens  changes  during  accommodation  is 
very  difficult  to  decide,  because  the  change,  if  it  exists,  does 
not  exceed  the  limit  of  an  error  of  observation.  Influenced, 
perhaps,  by  the  observation  of  Helmholtz,  I  had  thought  an 
increase  of  thickness  established.  Recently  I  took  up  the  subject 
anew  in  collaboration  with  Professor  Koster;  we  went  to  much 
trouble  without  being  able  to  reach  a  definite  result. 

87.  The  Author's  Theory  of  Accommodation. — After  the  ob- 
servations which  I  have  just  described  in  the  preceding  paragraph, 
and  which  can  be  briefly  expressed  by  saying  that  accommoda- 
tion is  effected  by  the  temporary  formation  of  an  anterior  lenti- 
conus,  the  hypothesis  of  Helmholtz  does  not  seem  tenable;  for 


CAB 

Fig.  122o. — Reflection  images  on  the  anterior  surface  of  the  dead  crystal- 
line lens.     A,  at  the  center;  B  and  C,  towards  the  borders. 

it  is  not  easy  to  conceive  how  such  a  mechanism  could  produce 
a  flattening  of  certain  parts  of  the  crystalline  lens  and  at  the 
same  time  an  increase  of  curvature  of  the  other  parts. 

I  have  already  observed  that  the  curvature  of  the  anterior 
surface  of  the  crystalline  lens  of  the  dead  eye  corresponds  with 
that  of  the  living  crystalline  lens  in  a  state  of  repose,  and  not 
at  all  with  the  accommodated  crystalline  lens.  But  the  difference 
between  the  dead  crystalline  lens  and  the  accommodated  crystal- 
line lens  is  still  more  striking,  if  we  consider  not  only  the  curva- 


ACCOMMODATION 


221 


ture  at  the  middle,  but  the  form  of  the  entire  surface,  because 
the  anterior  surface  of  the  accommodated  crystalline  lens  is 
flattened  towards  the  borders,  as  I  have  just  explained;  in  the 
dead  eye  the  curvature,  on  the  contrary,  increases  considerably 
towards  the  borders,  the  surface  having  the  form  of  an  ellipsoid 


Fig.  122&. — A,  the  dead  crystalline  lens;  B,  the  accommodated  crystalline 
lens.  The  dotted  lines  indicate  the  form  of  the  surfaces  of  the 
second  degree,  to  which  the  majority  of  crystalline  surfaces  most 
nearly  approach. 


of  revolution  around  the  short  axis.  This  fact,  which  was  al- 
ready established  by  Krause,  (i)  is  especially  very  striking  if 
we  examine  the  eye  with  the  ophthalmometer,  as  I  explained  on 


(1)  Helmholtz  seems  to  have  been  led  into  error  by  the  celebrated  measure- 
ments which  Jean  Louis  Petit  had  made  at  the  commencement  of  the  eighteenth 
century.  Most  of  the  measurements  of  Petit  are  very  exact,  but  those  of  the 
curvatures  of  the  surfaces  are  without  any  value.  He  had  a  series  of  copper 
plates  cut  in  the  form  of  arcs  of  circles  of  different  radii.  His  only  means  of 
determining  the  curvature  of  the  surfaces  of  the  eye  consisted  in  finding  the 
arc  of  the  circle,  which  seemed  to  him  to  conform  to  the  surface  .  The  measure- 
ments of  Krause  are  astonishingly  good  if  we  consider  the  manner  in  which 
he  made  them.  He  cut  a  fresh  eye  in  two,  along  the  axis,  placed  one-half  of 
it  in  water  under  a  micrometer  and  examined  with  a  microscope  of  little  magni- 
fying power. 


222  PHYSIOLOGIC  OPTICS 

page  74.  The  most  usual  way  is  to  remove  the  prism,  and  ob- 
serve the  image  of  the  keratoscopic  disc.  As  long  as  the  ophthal- 
mometer  is  placed  in  the  direction  of  the  axis  of  the  crystalline 
lens,  the  images  of  the  circle  are  round,  but,  if  we  displace  the 
instrument  so  as  to  form  the  image  near  the  border,  it  changes 
into  an  ellipse  with  the  long  axis  vertical.  Comparing  figure 
I22a  with  those  on  page  75,  we  see  that  the  deformity  of  the 
surface  is  quite  the  contrary  of  the  conical  form. — Following 
are  the  radii  of  curvature  from  5°  to  5°  of  an  eye  measured 
by  Holth,  compared  with  those  which  I  have  calculated  for  the 
eye  of  Demicheri  in  maximum  accommodation: 

Age        0°  5°  10o          150          20° 

Dead    eye 28     12.4mm.    12mm       Hmm         9mm          7mm 

Accommodated    eye. ...     25       5.6mm.      5.9mm      y.Qmm     18.0mm     79.2m.m 

We  see  that  we  can  scarcely  suppose  a  more  pronounced 
difference  (fig.  I22b).  I,  therefore,  set  myself  to  study  the 
physical  qualities  of  the  crystalline  lens,  by  using  especially  the 
lenses  of  horses,  which  are  very  large  and  consequently  easily 
handled,  and  I  have  found  that  we  cannot  consider  the  crystalline 
lens  as  a  simple  elastic  body  in  the  sense  of  Helmholtz.  The 
contents  of  the  crystalline  lens  are  composed,  in  the  adult,  of 
two  parts,  the  nucleus,  which  cannot  change  its  form,  and  the 
superficial  layer  which,  on  the  contrary,  possesses  this  faculty 
to  a  very  high  degree;  its  consistence  is  very  nearly  that  of  a 
solution  of  very  thick  gum.  I  call  this  layer  the  accommodative 
layer  in  order  to  show  that  it  is  due  to  it  that  the  eye  can  accom- 
modate itself.  According  as  age  advances,  the  nucleus  increases 
while  the  accommodative  layer  diminishes  and  with  it  the  am- 
plitude of  accommodation.  The  whole  is  surrounded  by  a  capsule 
which  is  inextensible  or  very  nearly  so  (Hocquard). 

It  has  always  been  supposed  that  a  traction  exerted  on  the 
zonula  must  flatten  the  crystalline  surfaces,  while  a  pressure 
exerted  on  the  borders  would  have,  on  the  contrary,  the  effect 
of  increasing  their  curvature.  Nothing  of  the  kind:  a  pressure 
exerted  on  the  borders  has,  on  the  contrary,  the  effect  of  flatten- 
ing the  surfaces,  while  a  traction  exerted  on  the  zonula  increases 


ACCOMMODATION 


223 


the  curvature  of  the  surfaces  at  the  middle,  while  flattening  them 
towards  the  periphery. 

To  verify  this  fact  we  take  the  crystalline  lens  from  the  eye 
of  an  ox  or  a  horse,  which  must  not  be  too  old,  with  the  capsule 
and  zonula  of  Zinn.  It  is  easy  to  see  that  by  compressing  the 
borders  the  surfaces  are  flattened;  to  observe  the  effect  of 
traction  we  take  hold  of  the  zonula  on  both  sides,  very  near  the 
crystalline  lens,  and,  by  pulling,  we  can,  on  looking  at  the  crys- 
talline lens  sideways,  see  that  the  anterior  surface  assumes  a 
hyperbolic  form  (fig.  123).  But  we  obtain  a  better  idea  of  the 
deformity  by  studying  the  catoptric  images.  We  place  the  crys- 
talline lens  with  the  anterior  surface  uppermost  on  a  table  and 
fix  above  it,  at  some  distance,  an  opaque  ring  on  which  we  have 
stretched  a  sheet  of  transparent  paper ;  by  illuminating  this  sheet 

of  paper  we  see  the  catop- 
tric image  of  the  ring 
formed  on  the  anterior  sur- 
face of  the  crystalline  lens 
as  a  black  circle.  We  can 
also  replace  the  ring  by  a 
big  lens.  The  size  and  dis- 
tance of  the  ring  must  be 
chosen  so  that  the  image 
may  be  sufficiently  large, 
and  placed  so  that  the  im- 
age may  be  centered  with 
the  crystalline  lens.  Then, 
by  exerting  a  traction  we 
see  the  circle  change  into 
an  oval,  the  short  axis  of 
which  corresponds  with  the 
direction  of  the  traction, 
which  proves  that  the  cur- 
vature increases  in  that  direction.  The  experiment  succeeds  the 
more  easily  the  larger  the  ring.  If  we  place  the  ring  so  that  its 
image  is  near  the  border  of  the  crystalline  lens,  we  see  it  lengthen 
in  the  direction  of  the  traction,  which  indicates  a  flattening  in  this 


Fig.  123. — Crystalline  lens  of  the  ox 
twice  enlarged:  The  dotted  line 
indicates  the  form  which  the  crys- 
talline lens  assumes:  A,  by  a 
lateral  pressure;  B,  by  a  traction 
exerted  on  the  zonula.  The  ar- 
rows indicate  the  direction  of  the 
forces. 


224  PHYSIOLOGIC  OPTICS 

direction.  Dr.  Crzellitzer  has  recently  constructed  an  instru- 
ment by  means  of  which  we  can  exert  a  traction  on  the  zonula 
in  all  directions  at  once,  and  with  which  we  can  still  better 
imitate  accommodation.  Instead  of  the  ring  we  may  use  two 
candles  placed  so  that  their  images  are  in  the  direction  of  the 
traction;  on  stretching  we  see  them  make  a  centripetal  move- 
ment analogous  to  the  movement  discovered  by  Cramer,  but 
much  less  extended.  Indeed,  on  the  one  hand,  it  is  probable  that 
these  animals  (i)  have  not  a  very  well  developed  accommoda- 
tion, and  on  the  other  hand,  it  must  not  be  forgotten,  that  in  the 
eye  the  displacement  appears  nearly  doubled  by  the  magnifying 
action  of  the  cornea.  The  experiment  can  be  considered  only  as 
an  imitation  of  accommodation  on  a  large  scale ;  but  the  fact  that 
we  can  obtain  an  increase  of  curvature  by  a  traction  exerted  on 
the  zonula  is  beyond  doubt. 

Furthermore,  we  should  scarcely  expect  any  other  result.  I 
have  several  times  emphasized  the  fact  that  the  nucleus  has  a 
much  more  pronounced  curvature  than  the  surfaces  of  the 
crystalline  lens,  and  moreover,  that  it 
cannot  change  its  form  unless  we  crush 
it.  Glancing  at  figure  124,  we  readily 
understand  that  by  exerting  a  traction 
on  the  zonula  the  peripheral  parts  must 
flatten,  while  at  the  middle  the  curvature 
increases  on  account  of  the  greater  re- 
sistance and  curvature  of  the  nucleus. 
And  the  result  will  be  the  same  if  there 
is  no  nucleus,  as  is  the  case  in  young  Fig.  124.— Opt^  system  of 
people,  only  if  the  curvature  and  resis-  the  eye  of  the  ox  (magni- 
tance  increase  towards  the  center.  The  fied  twice)- 


(1)  Dr.  Stadfeldt  later  verified  the  results  with  human  crystalline  lenses,  which 
he  placed  in  a  cork  ring,  fixing  two  opposite  parts  of  the  z6nula  with  very  fine 
needles.  He  measured  the  curvature  of  the  surfaces  with  the  ophthalmometer 
of  Javal  and  Schioetz,  and  then  determined  the  position  of  the  focus,  or  rather 
that  of  the  focal  lines,  with  a  microscope.  In  consequence  of  the  traction,  he 
always  caused  astigmatism,  the  maximum  of  curvature  corresponding  to  the 
direction  of  the  traction.  On  a  crystalline  lens  belonging  to  a  person  aged  38 
years,  he  thus  produced  an  astigmatism  of  the  anterior  surface  of  4  D.  The 
posterior  surface  was  only  very  slightly  influenced. — The  astigmatism  disappeared 
with  the  traction. 


ACCOMMODATION  225 

increase  of  curvature  of  the  central  layers  is  visible  on  any 
preparation  of  the  crystalline  lens.  The  increase  of  resistance 
finds  its  optic  expression  in  the  increase  of  index  towards  the 
center. 

By  traction  on  the  zonula  we  have  obtained  changes  analogous 
to  those  which  we  observe  during  accommodation,  and  it  seems 
to  me  that  the  structure  of  the  ciliary  muscle  lends  itself  very 
well  to  the  production  of  such  traction.  We  have  seen  that 
it  is  composed  for  the  most  part,  of  longitudinal  fibres,  that  the 
most  superficial  fibres  are  inserted  in  front  on  the  sclera,  near 
the  canal  of  Schlemm,  while  the  middle  fibres  end  free  near 
the  surface  which  lies  towards  the  anterior  chamber,  and  that 
the  deepest  fibres  are  combined  with  the  oblique  and  circular 
fibres  which,  perhaps,  form  their  terminations.  The  muscle  has 
the  form  of  a  little  triangle,  the  external  surface  of  which  rests 
on  the  sclera,  while  the  internal  surface  is  turned  towards  the 
vitreous  body  and  the  anterior  surface  towards  the  anterior 
chamber.  During  contraction  the  antero-external  angle  remains 
fixed,  the  antero-internal  angle  recedes,  as  we  can  see  directly 
in  the  anterior  chamber,  and  the  posterior  extremity  advances 
as  the  experiments  of  Hensen  and  Voelkers  prove.  The  reces- 
sion of  the  anterior  part  exerts  on  the  zonula  the  traction  which 
produces  the  deformity  of  the  anterior  surface ;  the  advancement 
of  the  posterior  extremity  exerts  on  the  choroid  a  traction  which 
has  the  effect  of  sustaining  the  vitreous  body  and  indirectly  the 
crystalline  lens,  so  that  the  latter  does  not  recede  under  the  in- 
fluence of  the  traction.  As  far  as  the  actual  result  is  concerned, 
it  matters  little  to  which  of  the  two  actions  we  attach  the  greater 
weight.  Let  us  conceive,  for  example,  a  moment  when  the  an- 
terior extremity  may  be  fixed:  the  result  of  the  contraction  of 
the  muscle  would  be  that  the  crystalline  lens,  on  account  of  the 
traction  exerted  on  the  choroid,  would  be  pushed  a  little  forward, 
which  would  produce  also  a  traction  on  the  zonula,  which  would 
suffice  for  the  deformity  of  the  crystalline  surface.  It  may  be 
that  there  exist,  in  this  relation,  individual  differences  as  the  dis- 


226  PHYSIOLOGIC  OPTICS 

agreement  between  the  observations  of  Helmholtz  and  my  ob- 
servations seems  to  indicate,  (i) 

I  think  that  this  theory  explains  quite  satisfactorily  the  greater 
part  of  the  phenomena  which  accompany  accommodation.  It 
explains,  in  the  first  place,  the  deformity  of  the  anterior  surface ; 
the  direction  of  the  zonula  in  the  living  eye  is  such  that  the 
effect  of  the  traction  must  act  almost  exclusively  on  the  anterior 
surface.  It  explains  also  the  change  of  level  of  the  iris  and  the 
diminution  of  tension  of  the  anterior  chamber  (by  the  recession 
of  the  peripheral  parts  of  the  crystalline  lens  and  iris). 

The  phenomena  observed  by  Cocdus  are  probably  due  to  an 
optic  illusion.  Holding  the  crystalline  lens  of  a  horse  in  front 
of  a  red  ground  we  see  this  color  through  the  whole  crystalline 
lens,  except  at  a  quite  narrow  border  where  the  red  rays  undergo 
total  reflection.  By  exerting  a  traction  on  the  zonula,  this  border 
enlarges  at  the  expense  of  the  transparent  part,  which  makes 
one  think  of  a  diminution  of  the  diameter  of  the  crystalline  lens. 

We  have  not  succeeded,  up  to  the  present,  in  explaining  satis- 
factorily the  singular  phenomena  which  I  observed  when  the  ac- 
commodation attained  its  maximum  (page  216).  I  had  attri- 
buted them  to  a  displacement  downwards  of  the  crystalline  lens, 
due  to  an  unequal  traction  on  the  zonula.  But  since  Hess  and 
Heine  have  shown  that  the  displacement  takes  place  following 
the  weight,  this  explanation  must  of  necessity  be  abandoned. 
Hess  supposes  that  the  crystalline  lens  falls  downwards  by  the 
relaxation  of  the  zonula,  as  stated  by  Helmholtz,  but  apart  from 
the  fact  that  the  hypothesis  of  Helmholtz  must  be  rejected  for 
other  reasons,  it  is  not  easy  to  any  longer  suppose,  in  view  of 
the  manner  in  which  the  crystalline  lens  is  fixed  on  the  vitreous 


(1)  According  to  certain  authors  (Arlt,  Iwanoff),  the  ciliary  muscle  differs  in 
myopes  and  hypermetropes.  If  this  is  so,  we  might,  perhaps,  find  the  predisposi- 
tion to  myoia  in  a  special  structure  of  the  ciliary  muscle.  It  is,  indeed,  clear 
that  the  more  the  superficial  fibres  are  developed  the  greater  must  be  the  traction 
exerted  on  the  choroid,  and  this  traction  has  evidently  for  its  object  the  protec- 
tion of  the  sclera  against  the  increase  of  tension  during  accommodation.  If  the 
posterior  extremity  of  the  muscle  were  fixed,  the  sclera  would  be  exposed  to  this 
tension  every  time  one  would  accommodate.  In  view  of  this  relation,  it  may 
be  interesting  to  observe  that  the  eye  which  I  examined,  in  which  the  anterior 
•urface  of  the  crystalline  lens  did  not  advance  during  accommodation,  is  myopic 
about  6  D.,  and  that  that  one  of  the  three  eyes  of  Helmholtz  which  showed  the 
least  advancement  was  slightly  myopic. 


ACCOMMODATION  227 

body,  'that  it  can  fall  downwards  unless  the  anterior  part  of  the 
vitreous  body  is  displaced  also.  The  fact  that  the  movement  of 
the  small  image  is  much  wider  than  that  of  the  large  one  (i), 
indicates  in  every  case  that  there  can  be  no  question  of  a  dis- 
placement directly  downwards,  but  rather  a  see-saw  movement 
downwards  and  backwards. — Among  other  explanations  which 
might  occur  to  us,  that  of  a  deformity  due  to  a  displacement 
of  the  crystalline  mass  in  the  interior  of  the  capsule  would  per- 
haps be  the  most  probable. 

f  As  to  the  contraction  of  the  pupil  which  accompanies  accom- 
modation, it  is  evident  that  it  has  the  effect  of  eliminating  the 
peripheral  parts  of  the  crystalline  lens,  which,  by  reason  of  their 
flattening,  would  render  the  image  too  poor.  We  know  also 
that  when  the  pupil  is  dilated  with  an  alkaloid  which  has  little 
or  no  effect  on  the  accommodation  (cocaine  or  homatropine) , 
near  sight  diminishes  relatively  more  than  far  sight;  this  phe- 
nomenon is  often  attributed  to  a  diminution  of  the  amplitude 
of  accommodation,  but  at  least  with  cocaine  I  have  only  very 
rarely  been  able  to  prove  a  real  diminution  of  this  amplitude. 
We  must  note,  however,  that  eyes  which  have  a  strong  spherical 
aberration  correct  this  aberration  by  accommodation;  these  eyes 
may,  therefore,  see  relatively  better  near  at  hand  than  far  away, 
when  the  pupil  is  dilated. 

When,  in  a  paracentesis,  we  allow  the  aqueous  humor  to  es- 
cape, we  know  that  the  crystalline  lens  and  the  iris  come  to  be 
applied  against  the  Cornea,  without  this  membrane  noticeably 
changing  form.  In  all  probability,  the  crystalline  lens  is  then 
in  the  state  of  highest  accommodation,  because  it  could  not  make 
such  a  movement  without  exerting  a  strong  traction  on  the 
zonula.  While  performing  paracentesis  on  a  rabbit's  eye,  Mann- 
hardt  claims  that  he  saw  also  the  accommodative  displacement 
of  the  images  of  Purkinje,  by  means  of  the  ophthalmoscope  of 
Cramer.  It  becomes  probable,  therefore,  that  the  pupillary  con- 

(1)  A  slight  displacement  of  the  look  downwards  would  give  analogous  phe- 
nomena. When  the  eye  makes  a  movement,  the  displacement  of  the  images  is  in 
direct  relation  with  the  distance  of  the  center  of  curvature  of  the  surface  in 
question  to  the  center  of  rotation  of  the  eye.  The  displacement  of  the  small 
image  is  relatively  large  because  the  center  of  curvature  of  the  posterior  surface 
of  the  crystalline  lens  is  situated  very  far  forward  in  the  eye. 


228  PHYSIOLOGIC  OPTICS 

traction,  which  accompanies  the  escape  of  the  aqueous  humor, 
is  accommodative.  But  the  pupillary  contraction  accompanies 
the  escape  of  the  aqueous  humor  even  in  a  dead  eye;  by  intro- 
ducing the  point  of  a  Pravaz  syringe  into  the  anterior  chamber, 
it  is  easy  to  dilate  or  contract  the  pupil  at  will  by  injecting  or 
removing  the  liquid.  This  contraction  is,  therefore,  pfurely 
mechanical,  and  it  then  becomes  probable  that  the  accommodative 
contraction  of  the  pupil  is  so  also,  although  this  mechanism  is 

not  yet  clearly  elucidated. 

ft 

Bibliography. — Petit  (J.  L.  Memoire  sur  e  crystallin  de  Voel  de 
I'homme.  Hist,  de  1'  Academic  des  Sciences,  1730. — Krause  (C.).  Pog- 
gendorf's  Annalen,  1834-36. — Max  Langenbeck.  Klinische  Beitrage  zur 
Chirurgie  und  Ophthalmologie.  Gottingen,  1849. — Cramer  (A.).  Het 
Accommodatievermogen  der  Oogen.  Haarlem,  1853.  Translated  into  Ger- 
man by  Doden.  Leer,  1855. — Helmholtz  (H.).  Ueber  die  Accommodation 
des  Auges.  Archiv  fiir  Ophtalmologie,  1,  2. — Grafe  (A.),  r  Fall  von 
acquirirter  Aniridie  als  Beitrag  zur  Accommoda,  tionslehre.  A.  f.  O.  VII, 
2,  p.  150. — Briicke  (E.).  Anatomische  Beschreibung  des  menschlichen 
Augapfels.  Berlin,  1847. — Bowman  (William).  Lectures  delivered  in  the 
London  Eoyal  ophthalmic  hospital.  Moorfields,  1847. — Miiller  (Heinrich). 
Ueber  einen  ringformigen  Muskel  am  CiliarTcorper  des  Menschen  und  uber 
den  Mechanismus  der  Accommodation.  A.  f.  O.,  Ill,  p.  1. — Mannhardt. 
Bemerlcungen  uber  den  AccommodationsmusTcel  und  die  Accommodation. 
Arch,  fur  Opht.,  IV,  1. — Hueck  (A.).  Die  Bewegung  der  Krystallinse. 
Leipzig,  1841. — Coccius  (A.).  Ueber  den  Mechanismus  der  Accommoda- 
tion des  menschlichen  Auges.  Leipzig,  1867. — Forster  (R.).  Zur  Kennt- 
niss  der  Accommodationsmechanismus.  Kl.  M.  f.  A.,  1864  p.  368. — Rochon- 
Duvignaud.  Eeclierches  sur  V angle  de  la  hambre  anterieure  et  le  canal  de 
Schlemm.  Paris,  Steinheil,  1892. — Tscherning  (M.).  Etude  sur  le  mecan- 
isme  de  I 'accommodation.  Arch,  de  phys.,  January,  1894. — L'optometre  de 
Young  et  son  emploi.  Arch,  de  Phys.,  October,  1894. — Eecherches  sur  les 
changements  optiques  de  I'oeil  pendant  I' accommodation.  Arch,  de  phys., 
January,  1895. — Theorie  des  changements  optiques  de  I'oeil  pendant  V ac- 
commodation. Arch,  de  phys.,  January,  1895. — Crzellitzer  (A.).  Die 
T  scheming  sche  Accommodationstheorie.  Grafe 's  Archiv.,  XLII,  4,  1896. — 
Stadfeldt  (A.).  Die  Verdnderung  der  Linse  bei  Traction  der  Zonula.  Kl. 
M.  f.  A.,  December,  1896. — Crzellitzer  (A.).  Zonularspannung  und  Linsen- 
form.  Bericht  der  Heidelberger  Gesellschaft,  1896. — Hess  (C.).  Arbeiten 
aus  dem  Gebiete  der  Accommodationslehre.  Grafe's  Archiv.,  1896-99. — 
Heine  (L.).  Die  accommodation  Linsenverschiebungen  im  Auge.  Grafe's 
Archiv,  1897. — Tscherning  (M.).  The  Theory  of  Accommodation.  Oph- 
thalmic Review,  April,  1899. — Tscherning  (M.).  La  surcorrection  accom- 
modative de  V 'aberration  de  sphericite  de  I'oeil.  Journal  de  Physiologic, 
March,  1899. 


CHAPTER  XIII 
OPHTHALMOSCOPY 

; 

88.  Methods  of  Illuminating  the  Fundus  of  the  Eye. — It  has 
been  known  from  the  remotest  times  that  the  pupil  of  certain 
animals  (dog,  cat,  etc.)  can  appear  luminous.  The  phenomenon 
was  thought  to  be  analogous  to  the  production  of  light  by  the 
glow-worm  (phosphorescence)  ;  in  reality  it  is  due  to  the  exist- 
ence of  the  tapetum,  a  part  of  the  choroid  the  retinal  surface  of 
which  is  strongly  reflecting  and  has  a  metallic  reflex ;  its  purpose 
is  not  very  well  elucidated.  As  to  the  human  pupil,  it  has  been 
known  for  a  long  time  that  it  may,  in  very  rare  cases,  appear 
luminous  after  the  development  of  an  anterior  tumor  of  the 
eye  (amaurotic  cats' -eye).  Beer  also  remarked  the  ocular  glow 
in  certain  cases  of  aniridia. 

Towards  1850  Gumming  and  Bruecke  discovered  the  method 
of  making  the  pupil  of  the  normal  eye  appear  luminous,  and 
HeUnholtz  in  1851  achieved  the  great  invention  of  the  ophthal- 
moscope which  was  destined  to  revolutionize  ophthalmology. 

Like  every  other  object  the  fundus  of  the  eye  sends  back  light 
when  it  is  illuminated.  Let  A  (fig.  125)  be  a  luminous  point 


Fig.  125. 

for  which  the  eye  is  accommodated.  This  point  sends  into  the 
eye  the  cone  ABC,  the  rays  of  which  reunite  at  D.  This  point, 
being  illuminated,  sends  the  rays  in  all  directions;  those  con- 
tained in  the  cone  ABC  emerge  from  the  eye  to  meet  at  a  point 
A.  Generally,  therefore,  the  eye  can  send  back  light  to  a  point 

229 


230  PHYSIOLOGIC  OPTICS 

which  has  first  sent  the  light  to  it,  and  if  in  ordinary  circum- 
stances the  pupil  of  the  eye  appears  black,  it  is  because  the  pupil 
of  the  observing  eye,  being  black,  cannot  send  light  back  into 
the  observed  eye.  In  order  that  it  may  appear  luminous,  a  lu- 
minous source  must  be  placed  in  front  of  the  observing  eye; 
this  is  what  we  do  by  means  of  the  ophthalmoscope. 

Following  are  the  different  circumstances  in  which  we  can 
see  the  pupil  luminous : 

a.  The  pupil  of  albinos  is  seen  red  because  the  fundus  of  the 
eye  is  illuminated  by  the  light  which  has  passed  through  the 
sclera.  If  we  cover  the  eye  with  a  screen  pierced  by  an  aperture 
corresponding  to  the  pupil,  the  latter  appears  black. — By  concen- 
trating a  bright  light  on  the  sclera  by  means  of  a  lens,  we  can 
make  the  pupil  of  a  normal  eye  luminous,  especially  if  the  person 
has  a  fair  complexion. 


Fig.  126. 

b.  If,  in  the  case  of  figure  125,  the  eye  is  not  exactly  focused 
for  the  luminous  point,  the  latter  illuminates  on  the  retina  a 
circle  of  diffusion  (ab,  fig.  126).  This  circle  sends  back  the 
light  not  only  in  the  direction  of  the  luminous  point,  but  also  in 
neighboring  directions:  thus  the  point  a  sends  back  the  cone 
BaC  which,  outside  the  eye,  takes  the  direction  ABCd,  so  that 
the  observing  eye  o  may  be  placed  in  this  cone.  Placing  a  lamp 
at  some  distance  from  the  observed  eye  and  sighting  near  the 
border  of  the  flame,  from  which  we  shelter  ourselves  by  a  screen, 
we  can  frequently  see  the  pupil  luminous,  especially  if  it  is  a 
little  large  and  if  the  patient  does  not  fix  the  flame. 

The  experiment  succeeds  more  easily  if  the  observed  eye  is 
strongly  ametropic,  because  then  the  rays,  having  emerged  from 
the  eye,  soon  diverge  greatly,  so  that  the  observing  eye  may 


OPHTHALMOSCOPY 


231 


easily  find  a  place  in  the  luminous  cone.  If  the  eye  is  not 
ametropic  we  can  make  it  so  by  means  of  a  strong  lens  or  by 
putting  it  under  water,  or,  as  Bellarminoff  has  lately  done,  by 
placing  a  plate  of  glass  in  contact  with  the  cornea  so  as  to  elimi- 
nate the  refracting  power  of  this  membrane.  By  this  latter 
means  we  can  make  the  fundus  of  the  eye  visible  for  several 
persons  at  once. — In  the  case  of  amaurotic  cafs-eye,  the  presence 
of  the  tumor  in  the  interior  of  the  eye  makes  the  latter  strongly 
hypermetropic,  so  that  the  fundus  becomes  easily  visible. 

c.  PRINCIPLE  OF  THE  OPHTHALMOSCOPE  OF  HELMHOLTZ. — Let 
AB  (fig.  127)  be  a  plate  of  plane,  parallel  glass  and  L  a  lamp 
which  sends  light  towards  this  plate.  The  greater  part  of  the 
light  passes  through  the  plate,  but  a  part  is  reflected  towards 
the  observed  eye,  D.  It  enters  this  eye  and  illuminates  the  retina. 
The  latter  sends  back  light  towards  the  plate :  a  part  of  this  light 
is  reflected  towards)  the  lamp  L,  but  the  greater  part  passes 
through  the  plate  and  enters  the  observing  eye  C,  which,  conse- 
quently, sees  luminous  the  pupil  of  the  observed  eye.  To  corn- 


Fig.  127. — Principle  of  the  ophthalmoscope  of  Helmholtz. 

pensate  for  the  loss  of  light  which,  proceeding  from  L,  passes 
through  the  plate,  Helmholts  used  several  plates,  placed  one  be- 
hind the  other. 


232  PHYSIOLOGIC  OPTICS 

d.  PRINCIPLE  OF  THE  ORDINARY  OPHTHALMOSCOPE. — We  ob- 
tain a  more  intense  illumination  by  means  of  a  silvered  mirror; 
the  observer  looks  through  a  small  portion  from  which  the  coat- 
ing has  been  removed  or  which  has  been  perforated. — As  a 
concave  mirror  concentrates  the  light  it  illuminates  better  than 
a  plane  mirror,  and  the  latter  better  than  a  convex  mirror,  (i) 
Generally  it  is  useful  to  have  a  good  illumination ;  but  we  some- 
times see  better  the  very  delicate  changes  in  the  fundus  of  the 
eye  by  using  a  weak  illumination,  and  very  delicate  opacities  of 
the  vitreous  body  or  of  the  crystalline  lens  disappear  if  the 
illumination  is  too  strong. 

The  ophthalmoscope  is  the  only  practical  means  of  illuminating 
the  eye.  Nevertheless,  a  different  method  may  sometimes  prove 
serviceable.  We  place  the  lamp  behind  the  observer  so  that  the 
light  reaches  the  observed  eye  by  glancing  along  the  head  of  the 
observer ;  we  concentrate  the  light  on  the  eye  with  a  lens.  When 
the  pupil  is  dilated  we  can  thus  see  the  fundus  of  the  eye  feebly 
illuminated,  and  we  often  distinguish  details  situated  far  forward 
in  the  vitreous  body  (tumors  of  the  ciliary  body,  detachments, 
etc.). 

89.  Examination  by  the  Erect  Image  (Helmholtz). — The  con- 
ditions for  seeing  the  pupil  luminous  were  known,  before  Helm- 
holtz, by  the  researches  of  Gumming  and  Bruecke,  and  Babbage 
seems  to  have  already  illuminated  the  pupil  with  a  mirror  from 
a  small  portion  of  which  the  coating  was  removed  for  observa- 
tion purposes;  but  none  of  these  scientists  thought  of  studying 
the  conditions  under  which  this  ocular  glow  can  form  an  image 
of  the  fundus  of  the  eye. 

When  preparing  the  lectures,  in  the  course  of  which  he  was 


(1)  The  clearness  of  the  retinal  image  of  the  flame  which  is  formed  in  the 
observed  eye  is  the  same  in  all  cases,  but  the  image  is  larger  when  we  use  a 
concave  mirror  than  when  we  use  a  plain  or  convex  mirror. — One  can  verify  this 
for  oneself  by  putting  one's  eye  in  the  place  of  the  observed  eye.  The  image 
of  the  flame  which  one  then  sees  in  /the  mirror  corresponds  to  the  illuminated 
part  of  the  retina ;  it  is  larger  in  the  case  of  the  concave  mirror  than  with  the 
plane  or  convex  mirror. — Placing  the  flame  behind  the  mirror,  one  sees,  in  the 
same  circumstances,  the  opening  as  a  luminous  circle  which  corresponds  to  the 
part  of  the  fundus  of  the  eye  which  the  observer  can  see  at  once  (ophthalmoscopic 
field). 


OPHTHALMOSCOP¥  233 

to  illustrate  for  his  class  the  methods  of  making  the  pupil  ap- 
pear luminous,  Hehnholtz  proposed  to  himself  the  problem  to 
be  solved,  not  a  difficult  task  for  an  experienced  physicist.  He 
easily  succeeded  in  solving  it  theoretically,  and  then  constructed 
the  first  ophthalmoscope  by  combining  some  glass  plates  with 
the  lenses  of  a  test  case ;  after  some  days  of  hard  work  he  suc- 
ceeded in  seeing  the  fundus  of  the  living  eye  which  no  one  had 
ever  seen  before  him. 

Helmholtz  used  examination  by  the  erect  image.  Suppose  that 
the  observer  is  emmetropic  (if  he  is  not  he  must  correct  his  re- 
fraction) :  he  can  then  see  the  fundus  of  the  eye  of  another 
emmetrope  without  any  further  aid,  since  the  rays  emerging 
from  the  observed  eye  are  parallel.  If  the  observed  person  is 
not  emmetropic  he  must  be  made  emmetropic.  We,  therefore, 
look  for  the  strongest  convex  glass  or  the  weakest  concave  glass 
with  which  we  can  see  the  fundus  of  the  eye  distinctly:  this 
glass  indicates  at  the  same  time  the  refraction  of  the  eye;  but 
the  observer  must  cultivate  the  habit  of  not  using  his  accommo- 
dation, otherwise  the  results  will  be  false. — The  refraction  which 
we  find  with  the  ophthalmoscope  ought  to  be  in  agreement  with 
that  found  by  subjective  examination.  It  must  be  noted,  how- 
ever, that  the  glass  of  the  ophthalmoscope  is  generally  a  little 
farther  away  from  the  eye  examined  than  a  glass  placed  in  a 
frame.  We  find,  therefore,  as  by  the  subjective  method,  too 
low  a  number  for  hypermetropia,  too  high  a  number  for  myopia, 
and  the  error  is  more  pronounced  in  the  case  of  an  ophthalmo- 
scopic  examination  on  account  of  the  greater  distance.  For 
low  degrees  of  ametropia  it  is  insignificant;  for  high  degrees, 
especially  of  myopia,  it  is  sufficient  to  make  the  determination 
fallacious.  Latent  hypermetropia  is  generally  disclosed  by 
ophthalmoscopic  examination  because  in  the  dark  room  the 
patients  do  not  fix. 

MAGNIFICATION. — To  obtain  a  numerical  expression  of  opb- 
thalmoscopic  magnification,  we  may  compare  the  retinal  image, 
formed  in  the  observing  eye,  of  an  object  (the  papilla  of  the 
fundus  of  the  examined  eye)  with  the  retinal  image  which  the 
observing  eye  would  have  of  the  same  object,  placed  free  in  air, 


234 


PHYSIOLOGIC  OPTICS 


at  the  working  distance  of  the  observer.  We  often  make  this 
distance  20  centimeters. 

Let  us  suppose  that  both  eyes,  that  of  the  observer  and  that 
of  the  observed  person,  are  emmetropic. 

Let  O=AB  (fig.  128)  be  the  object  of  the  fundus  of  the  ob- 
served eye;  we  draw  the  rays  AC  and  BD  parallel  to  the  axis. 
These  two  rays  will  intersect  at  the  anterior  focus  $19  and  all  the 


Patient 


Observer 


Fig.  128. 


other  rays  proceeding  from  A  and  B  are  parallel  to  either  of 
these;  among  other  rays  ^E  and  &\G  which,  prolonged,  pass 
through  the  anterior  focus  of  the  observing  eye.  After  refrac- 
tion in  this  eye  these  rays  are  parallel  and  determine  the  size  of 
the  image,  I.  Designating  by  Fl  the  anterior  focal  distance  of 
the  observed  eye,  by  F/1  that  of  the  observing  eye,  the  two 


similar  triangles 


and 


give  the  relation: 


I       F'i 
7TT 


We  see  that,  if  the  optic  systems  of  both  eyes  are  alike,  I  is 
equal  to  O.  The  papilla  of  the  observed  eye  forms  in  the  ob- 
serving eye  an  image  equal  to  itself.  By  placing  the  fundus  of 
the  eye  free  in  the  air  at  the  working  distance,  equal  to  20  centi- 
meters, the  retinal  image  Ij  of  the  object  O  (fig.  129)  would 
be  found  by  the  formula 


200 


By  multiplying  this  formula  by  the  preceding  one,  we  obtain 
the  magnification  in  the  erect  image: 

I        200mm 


OPHTHALMOSCOPY 


235 


By  supposing  15  millimeters  for  F1,  the  magnification  would 
be  about  13,  but  this  number  is  arbitrary,  since  the  working 
distance  has  been  chosen  arbitrarily. 


Fig.  129. 


Observer 


If  the  observed  eye  is  myopic,  the  magnification  is  greater, 
supposing  that  the  correcting  glass  is  beyond  the  anterior  focus 
of  the  observed  eye,  as  is  always  the  case.  The  construction 
is  the  same  as  in  the  preceding  case,  but  on  meeting  the  con- 
cave glass  the  rays  C*j_  and  D$x  (fig.  130)  are  made  more 


Patient 


Fig.  130. 


divergent.  The  rays  &\E  and  &\G  which  are  parallel  to  them 
diverge,  therefore,  more  than  in  the  preceding  case,  which 
makes  the  image  Ij  greater.  If  there  is  a  case  of  myopia  of 
curvature  the  magnification  is  still  greater;  the  point  <£t  is,  in 
fact,  situated  nearer  the  observed  eye,  which  causes  the  rays 
HK  and  LM,  and  consequently  also  the  rays  $/1E  and  ^>'1G 
to  diverge  still  more.  In  the  hypermetropic  eye  the  reverse 
takes  place.  It  follows  that  in  an  astigmatic  eye  we  see  the 
papilla  elongated  in  the  direction  of  the  meridian  of  greatest 
refraction. 

OPHTHALMOSCOPIC  FIELD. — According  to  Helmholtz  we  find 
the  ophthalmoscopic  field,  that  is  to  say,  the  aggregate  of  the 


236  PHYSIOLOGIC  OPTICS 

parts  of  the  fundus  of  the  eye,  visible  simultaneously  by  join- 
ing by  straight  lines  the  middle  of  the  pupil  of  the  observing 
eye  to  the  borders  of  the  pupil  of  the  observed  eye,  and  by 
making  these  straight  lines  undergo  the  same  refraction  in  the 
observed  eye  as  if  they  were  rays.  Figure  131  shows  that  the 
field  is  greater  in  the  hypermetropic  eye,  smaller  in  the  myopic 
eye,  if  the  observing  eye  is  beyond  the  anterior  focus  of  the 
observed  eye,  as  is  always  the  case.  As  it  is  the  border  of  the 
pupil  of  the  observed  eye  which  limits  the  field,  we  increase  it 
by  instilling  atropine. 


Patient  Observer 

Fig.  131. — Construction  of  the  ophthalmoscopic  field. 

This  is  an  instance  of  inverse  constructions  which  we  fre- 
quently use  in  geometric  optics;  to  know  what  points  of  the 
fundus  of  the  observed  eye  can  send  back  rays  into  the  pupil 
of  the  observing  eye,  we  reverse  the  problem  by  imagining  the 
pupil  of  the  observing  eye  luminous  and  finding  what  parts  of 
the  fundus  of  the  observed  eye  it  can  illuminate.  The  result 
is  the  same  on  account  of  the  reversibility  of  the  optic  pro- 
cesses. In  reality  the  field  is  a  little  larger  than  that  which  we 
have  found  by  our  construction,  since  we  have  reduced  the 
pupil  of  the  observing  eye  to  a  point ;  from  the  point  d,  situated 
outside  the  field,  some  rays  could  still  enter  the  observing  eye 
through  the  lower  parts  of  the  pupil.  To  have  the  field  com- 
plete it  would  be  necessary  to  construct,  not  the  image  p^  of 
the  center  of  the  pupil  p,  but  the  image  of  the  entire  pupil  or 
rather  of  the  opening  of  the  ophthalmoscope,  formed  by  the 
optic  system  of  the  observed  eye.  We  would  thus  obtain  a 
larger  field,  but  the  parts  near  the  border  would  be  very  slightly 
illuminated. 


OPHTHALMOSCOPY  237 

90.  Examination  by  the  Erect  Image.  Observations. — To  tell 
the  size  of  intra-ocular  objects,  it  is  customary  to  compare 
them  with  the  diameter  of  the  papilla;  we  thus  say  that  the 
width  of  a  staphyloma  is  the  fourth  or  half  of  the  diameter 
of  the  papilla.  The  attempts  which  have  been  made  to  obtain 
more  exact  measurements  by  means  of  a  micrometer  (Bonders, 
Leroy)  have  not  given  practical  results. 

The  refraction  is  usually  the  same  for  the  entire  fundus  of 
the  eye.  According  to  Young,  if  we  suppose  a  sphere  drawn 
around  the  eye  with  the  distance  of  the  far  point  as  radius*, 
the  position  of  the  retina  is  such  that  it  is  everywhere  found 
at  the  place  where  the  best  images  of  objects  situated  on  this 
sphere  would  be  formed.  A  certain  degree  of  astigmatism  by 
incidence  is  inevitable  for  the  peripheral  parts;  but  the  retina 
is  here  found  between  the  two  focal  lines  almost  at  the  place 
which  would  correspond  with  the  circular  diffusion  spot. 

Thanks  to  this  arrangement,  we  can  use  the  papilla  for  the 
determination  of  refraction  by  the  erect  image;  generally  its 
refraction  scarcely  differs  from  that  of  the  macula.  There  are 
exceptions  to  this  rule,  however.  For  instance,  I  examined 
on  consultation  a  young  man  in  whom  a  myopia  of  4  D.  was 
indicated,  while  a  colleague,  very  experienced  in  determination 
by  the  erect  image,  and  myself  found,  each  for  himself,  em- 
metropia  by  the  ophthalmoscope.  It  was  later  established  be- 
yond doubt  that  the  patient  had  really  a  myopia  of  4  D.  Then, 
asking  ourselves  whether  the  myopia  might  not  be  due  to  a 
spasm  of  accommodation,  we  resorted  to  a  treatment  by  atro- 
pine,  but  without  changing  the  result.  Analogous  differences 
seem  quite  frequent  in  cases  of  excessive  myopia,  by  reason 
of  the  elongated  form  of  the  globe. 

A  difference  between  subjective  and  ophthalmoscopic  refrac- 
tion may  therefore  be  due:  i°  to  a  greater  distance  of  the 
correcting  glass  from  the  observed  eye  (see  page  234) ;  2°  to 
the  fact  that  a  latent  hypermetropia  may  become  manifest  in 
the  darkness;  3°  to  the  fact  that  the  papilla  may  have  a  dif- 
ferent refraction  from  the  macula;  4°  to  stimulation. 

To   judge  of  the   depth  of   a   papillary   excavation   we  can 


238  PHYSIOLOGIC  OPTICS 

measure  the  difference  of  refraction  between  the  edge  and  pit 
of  the  excavation,  keeping  in  mind  that  a  difference  of  one 
dioptry  corresponds  to  almost  a  third  of  a  millimeter.  We  can 
measure  by  the  same  process  the  tumefaction  of  the  papilla  in 
cases  of  optic  neuritis,  the  distance  of  an  opacity  of  the  vitreous 
body  from  the  retina,  etc. 

Another  means  of  judging  whether  one  point  is  situated  in 
front  of  another  consists  in  making  slight  movements  of  the 
head  (with  the  ophthalmoscope).  We  shall  then  see  the  nearer 
point  make  a  movement  in  a  contrary  direction  in  relation  to 
the  other  point  (parallax). 

The  magnification  of  13  which  we  have  found  for  the  erect 
image  has  nothing  to  do  with  the  apparent  size  of  the  papilla, 
which  depends  on  the  distance  to  which  we  project  the  image 
without  knowing  it.  When  we  begin  to  use  the  ophthalmoscope, 
the  papilla  frequently  appears  very  small,  and  generally  its  size 
seems  to  vary  for  different  observers.  I  have  noticed  a  phe- 
nomena of  the  same  kind  when  looking  at  a  luminous  point 
(see  page  165).  If  the  point  is  very  distant  the  circle  of  dif- 
fusion appears  very  large  to  me.  But  if  I  observe  a  luminous 
point  placed  at  the  focus  of  a  lens  of  2oD.,  held  in  front  of 
my  eye,  the  point  appears  extremely  small,  and  this  although 
the  retinal  image  ought  to  be  exactly  the  same  in  both  cases. 
Accommodation  is  often  charged  with  playing  a  part  in  this 
optic  illusion,  but  we  must  observe  that  it  takes  place  even  if 
every  trace  of  accommodation  be  excluded.  It  rests  on  an  un- 
conscious conclusion  relatively  to  the  distance  of  the  object  (see 
chapter  XXII). 

The  macula  is  usually  difficult  to  see:  most  frequently  the 
pupil  must  be  dilated.  The  fovea  is  sometimes  visible  as  a 
dark  spot  with  a  small  whitish  point  in  the  middle;  its  place  is 
marked  in  every  case  by  the  peculiar  manner  in  which  the 
vessels  come  from  all  sides  to  disappear  in  its  vicinity.  We 
never  see  a  trace  of  the  yellow  color  which  is  so  striking  in 
the  dead  eye ;  certain  authors  have,  therefore,  considered  this 
yellow  coloration  as  a  phenomenon  due  to  changes  after  death, 
and  this  idea  seems  confirmed  by  an  observation  which  I  have 


OPHTHALMOSCOPY  239 

made.  We  generally  suppose  that  if  we  do  not  see  the  yellow 
color  of  the  macula,  it  is  because  the  yellow  light  is  drowned 
by  the  red  light  reflected  by  the  blood.  I,  therefore,  thought 
that  we  should  be  able  to  see  it  by  illuminating  the  eye  with 
a  strong  sodium  flame.  The  blood  does  not  reflect  this  light  or 
reflects  it  only  slightly,  and  the  appearance  of  the  fundus  of 
the  eye  recalls  that  of  photographic  illustrations  of  ophthalmo- 
scopic  images;  we  see  the  vessels  black  on  a  gray  ground,  but 
the  macula,  which  we  should  expect  to  find  illuminated,  remains 
at  least  as  dark  as  in  ordinary  ophthalmoscopy. 

The  red  color  of  the  fundus  of  the  eye  is  due  to  the  vessels 
of  the  choroid;  wherever  the  choroid  is  defective  we  see  the 
white  background  of  the  sclera,  in  cases  of  coloboma  for  ex- 
ample. It  is  curious  that  we  never  see  a  trace  of  the  retinal 
purple  with  the  ophthalmoscope.  In  the  normal  state  the  retina 
is  completely  transparent;  we  see  only  its  vessels.  Sometimes 
we  can,  however,  distinguish  it  as  a  grayish  veil  in  the  parts 
near  the  papilla.  If  the  black  pigment  be  strongly  developed, 
the  fundus  of  the  eye  appears  of  a  uniform  deep  red.  If  it  is 
but  slightly  developed,  the  fundus  has  often  a  marble  or  spotted 
appearance  due  to  the  meshes  of  the  vascular  network  of  the 
choroid. 

Most  normal  eyes  have  a  physiologic  excavation  or  cup  of  the 
papilla  which  has  the  appearance  of  a  whitish  spot.  It  is  then 
easy  to  see,  by  the  erect  image,  that  the  bottom  is  more  myopic 
than  the  border ;  we  see  indistinctly  the  vessels  of  the  excavation 
when  those  of  the  borders  appear  distinct  and  vice  versa,  at 
least  when  the  excavation  is  a  little  deep.  The  physiologic  cup 
never  reaches  the  borders  of  the  papilla.  We  can  be  certain 
that  an  excavation  is  pathologic  only  when  it  reaches  the  borders 
everywhere. 

We  frequently  perceive  in  the  normal  eye  a  pulsation  of  one 
or  several  of  the  large  veins.  During  the  systole  the  tension 
of  the  globe  increases  enough  to  compress  the  large  veins  near 
their  starting  place  where  the  intra-venous  tension  is  weakest. 


240  PHYSIOLOGIC  OPTICS 

At  the  moment  of  diastole  the  tension  of  the  globe  diminishes, 
the  pressure  ceases  and  the  veins  empty  themselves,  (i) 

The  pulsation  of  the  arteries  is  nearly  always  a  sign  of 
glaucoma;  the  tension  of  the  globe  is  so  high  that  the  arteries 
remain  empty,  except  at  the  moment  of  systole. 

The  papilla  is  generally  limited  by  a  very  thin  white  border, 
sometimes  surrounded  by  an  incomplete  black  border,  formed 
by  the  pigment  of  the  choroid.  The  white  border  is  called  the 
scleral  border;  it  is  attributed  to  the  visibility  of  the  sclera 
between  the  choroid  and  the  papilla.  Sometimes  it  is  larger 
and  mistaken  for  an  incipient  staphyloma. 

One  can  see  the  red  fundus  of  one's  own  eye  by  looking  in 
a  mirror  held  before  a  flame.  A  luminous  pencil  passes  through 
the  opening  of  the  ophthalmoscope,  enters  the  eye,  is  reflected 
by  the  retina,  emerges  from  the  eye,  meets  the  mirror,  and  is 
again  reflected  towards  the  retina.  If  the  course  of  the  rays 
permit,  for  example  if  the  eye  is  emmetropic  and  the  mirror 
plane,  we  may  even  distinguish  the  details.  We  see  at  the 
same  time  the  catoptric  image  of  the  cornea  as  a  large  circle 
of  diffusion. 

Auto-ophthalmoscopes  have  been  constructed  as  well  as  oph- 
thalmoscopes, by  means  of  which  several  observers  can  see 
simultaneously  the  fundus  of  the  eye. 

Another  way  of  examining  oneself  consists  in  observing  with 
one  eye  the  image  of  the  other  formed  by  a  looking-glass;  we 
can  in  this  way  perform  ophthalmoscopy  of  the  left  eye  with 
the  right  eye  by  the  inverted  image,  and  we  can,  with  a  small 
concave  mirror  placed  not  far  from  the  eye,  observe  the  images 
of  Pnrkinje,  etc.  It  was  by  working  thus  with  my  own  eye  that 


(1)  [Lately  Dr.  S.  Turk  has  studied  this  question  again  in  a  number  of  persons 
with  irregular  heartbeat  (arythmia). 

These  observations  prove  that  the  venous  narrowing  is  independent  of  the  en- 
trance of  the  arterial  pulse  wave  into  the  eye,  and  he  infers  that  the  cardiac 
systole  produces  not  the  narrowing,  but  the  dilatation  of  the  veins.  He  further 
shows  that  this  venous  pulsation  cannot  be  caused  by  a  rhythmic  interference 
with  the  exit  of  the  blood  from  the  vena  centralis  retinae  because  a  dilatation, 
caused  in  this  way,  ought  to  be  propagated  opposite  to  the  direction  of  the 
blood-current.  He,  therefore,  considers  this  phenomenon  caused  by  a  propagation 
of  the  arterial  pulse  wave  through  the  capillaries  into  the  veins  which  is  ac- 
counted for  by  the  relatively  high  extravascular  pressure  in  the  eye  (Engelmann's 
Arch.  f.  Physiol.,  1899).] — W. 


OPHTHALMOSCOPY 


241 


I  observed  for  the  first  time  the  conical  deformity  of  the  an- 
terior surface  of  the  crystalline  lens  during  accommodation 
(page  210). 

i 

91.  Examination  by  the  Inverted  Image.— This  examination 
was  introduced  into  oculistic  practice  by  Ruete  in  1852.  It 
was  especially  adopted  and  developed  by  the  Berlin  school 
(Graefe),  while  the  Vienna  school  (Jaeger)  especially  used  the 
erect  image.  As  the  Berlin  school  held  for  a  long  time  a  more 
influential  position,  examination  by  the  inverted  image  was  for 
a  long  time  more  used  than  the  other.  The  two  methods,  how- 
ever, merit  a  place  side  by  side.  The  inverted  image  gives  a 
less  magnification  and  a  larger  field :  it  is,  therefore,  very  useful 
for  studying  the  general  appearance  of  the  fundus  of  the  eye, 
while  the  erect  image  serves  especially  for  the  study  of  the  de- 
tails and  for  the  determination  of  refraction. 

Examination  by  the  inverted  image  is  made  by  holding  a  strong 
convex  lens  (most  frequently  +13)  at  a  distance  from  the  eye 
almost  equal  to  its  focal  distance.  This  lens  forms  a  real  and 


Fig.  132. 

inverted  image  of  the  fundus  of  the  eye,  situated  on  the  other 
side  of  the  lens,  in  the  vicinity  of  its  second  focus.  It  is  this 
image  that  the  observing  eye  sees  when  accommodating,  or,  which 
is  better,  by  looking  through  a  convex  lens  of  about  4  D.,  placed 
behind  the  mirror.  If  the  examined  eye  is  emmetropic,  the 
rays  leaving  the  eye  are  parallel  and  the  image  is  formed  at 
the  focus  of  the  lens ;  if  it  is  myopic  the  image  is  a  little  nearer, 
if  hypermetropic  a  little  farther  than  the  focus.  In  the  latter 


242 


PHYSIOLOGIC  OPTICS 


case  the  observer  is  frequently  obliged  to  move  back  a  little  in 
order  to  see  the  image  distinctly. 

MAGNIFICATION. — If  we  use  a  lens  of  +13,  the  magnification 
is  about  five  times  for  an  emmetropic  eye.  Let  ab=O  (fig.  132) 
be  an  object  in  the  fundus  of  the  observed  eye.  We  draw  the 
ray  be  parallel  to  the  axis:  it  passes,  after  refraction,  through 
the  anterior  focus  of  the  eye  <E>X,  and  the  other  rays  coming  from 
b  are  parallel  to  it,  since  the  eye  is  emmetropic.  One  of  these 
rays  db'  passes  without  refraction  through  the  optic  center  of 
the  lens,  and  it  is  on  this  ray  db'  that  the  image  b'  of  b  is  formed, 
in  the  focal  plane  of  the  lens.  The  two  triangles  pc^1  and  dfb' 
are  similar:  we  have,  therefore,  iZ^J^.,  that  is  to  say,  the  mag- 

pc       p4>i 

nification  is  equal  to  the  relation  between  the  focal  distance  of 
the  lens  and  the  anterior  focal  distance  of  the  eye.  The  an- 
terior focal  distance  of  the  eye  being  15  millimeters  and  that  of 
the  lens  77  millimeters,  the  magnification  is  2L  or  about  5.  We 
can  increase  the  magnification  by  using  a  weaker  lens,  but  the 
image  at  the  same  time  moves  away  from  the  lens  so  that  the 
observer  is  obliged  to  move  back,  which  makes  this  way  of  in- 
creasing the  image  of  little  practical  value.  In  cases  of  persons 
operated  on  for  cataract  it  may  be  useful  to  use  a  stronger  lens 
(_j_i8)  to  obviate  the  necessity  of  moving  away. 


A 


M  £   H 


V 

Fig.  133. — After  Bjerrum. 


INFLUENCE  OF  REFRACTION  OF  THE  EXAMINED  EYE  ON  THE 
MAGNIFICATION. — A  glance  at  figure  133  suffices  to  show  that  if 
we  place  the  lens  so  that  its  focus  coincides  with  the  anterior 


OPHTHALMOSCOPY  243 

focus  of  the  eye,  the  magnification  is  the  same  whatever  may  be 
the  refraction  of  the  examined  eye  (principle  of  Badal).  (i) 

If  the  lens  is  nearer  the  eye,  as  is  generally  the  case,  the  mag- 
nification is  greater  in  the  hypermetropic  eye,  less  in  the  myopic 
eye  (fig.  134).  For  this  reason  the  papilla  of  the  astigmatic  eye 


M      E 


Fig.  134. — After  Bjerrum. 

is  seen  elongated  in  the  direction  of  the  meridian  of  least  re- 
fraction ;  by  moving  the  lens  away  the  other  meridian  is  elongated 
and  finally  that  which  corresponds  to  the  meridian  of  greatest 
refraction  is  seen  to  be  the  greater  just  as  by  the  erect  image. 

OPHTHALMOSCOPIC  FIELD. — In  order  that  the  field  may  be  as 
large  as  possible,  the  lens  must  be  at  a  distance  from  the  eye 
almost  equal  to  its  focal  distance.  Under  these  circumstances 
the  image  which  the  lens  forms  of  the  pupil  of  the  observed 
eye  is  very  large  and  fills  the  entire  lens;  the  iris  disappears 
from  the  field. 

We  construct  the  field  as  for  the  erect  image,  by  supposing 
the  center  (P,  fig.  135)  of  the  pupil  of  the  observing  eye  lumin- 
ous and  finding  what  part  of  the  fundus  of  the  eye  it  could 
illuminate.  In  drawing  figure  135,  it  has  been  supposed  that 
the  image  Pl  of  the  center  of  the  pupil  of  the  observer  coincides 
with  the  nodal  point  K  of  the  observed  eye,  so  that  the  "rays" 
Aa  and  Eb  suffer  no  refraction :  ab  is  therefore  the  field,  and  we 


(1)  This  is  exact  only  if  the  ametropia  is  axial.  In  case  of  a  myopia  (hyper- 
metropia)  of  curvature,  the  anterior  focus  is  situated  near  the  eye  in  proportion 
as  the  refraction  is  greater. — Repeating  the  construction  of  figure  133,  we  see 
that  by  making  the  focus  of  the  lens  coincide  with  the  anterior  focus  of  the  eye 
the  magnification  is  greater  in  the  case  of  myopia. — The  astigmatic  eye  has  two 
anterior  foci,  one  for  each  principal  meridian  ;  to  obtain  the  same  magnification 
in  both  meridians,  the  focus  of  the  lens  must  be  nearer  the  eye  than  the  more 
distant  anterior  focus. 


244 


PHYSIOLOGIC  OPTICS 


note  that  it  does  not  depend  on  the  pupil  of  the  observed  eye, 
since  the  cone  A'PjB  does  not  touch  its  borders.  The  field  is 
limited  only  by  the  borders  of  the  lens ;  it  is  therefore  preferable 
to  use  a  large  lens  as  they  do  in  England.  If  we  move  the  lens 
nearer  or  farther  away,  so  that  a  larger  part  of  the  cone  APtB 
coincides  with  the  pupil,  it  may  happen  that  the  latter  may  be 
too  small,  so  that  the  iris  intercepts  the  most  peripheral  rays. 
The  field  is  then  limited  by  the  iris  of  the  observed  eye,  which 
may  be  seen  through  the  lens.  If  the  pupil  is  small,  it  may  be 
difficult  to  hold  the  lens  exactly  at  the  proper  place  for  the 
iris  to  disappear;  this  is  why  dilation  of  the  pupil  is  advantag- 
eous.— It  must  be  noted,  furthermore,  that  a  small  part  of  the 


Patient  Observer 

Fig.  135. — Construction  of  the  ophthalmoscopic  field  by  the  inverted  image. 

field  is  well  illuminated.  If  we  use  a  concave  mirror  of  20 
centimeters  focus,  as  is  customary,  we  see  at  the  fundus  of 
the  eye  a  quite  distinct  image  of  the  flame  (because  the  image 
formed  by  the  mirror  is  almost  at  the  focus  of  the  lens  so  that 
the  rays  which  meet  the  eye  are  almost  parallel)  ;  it  is  only  the 
part  of  the  field  which  corresponds  to  this  image  that  is  illumi- 
nated; the  remainder  is  in  darkness. — The  illuminated  portion 
may  be  increased  by  using  a  plane  mirror,  but  the  illumination 
is  then  less  bright. 

We  can  see  the  inverted  image  without  any  lens  if  the  patient 
is  myopic  more  than  6  D. ;  by  moving  the  head  from  side  to  side, 
we  make  sure  that  the  vessels  are  displaced  in  the  contrary  di- 
rection, for  we  can  also  see  the  fundus  of  the  hypermetropic 
eye  (by  the  erect  image)  at  a  sufficiently  great  distance.  The 


OPHTHALMOSCOPY  245 

visual  field  is  very  small  and  the  magnification  often  so  great 
that  one  vessel  may  fill  half  of  the  field.  The  existence  of  this 
image  is  sufficient  to  establish  the  diagnosis  of  a  strong  myopia. 
—It  is  often  difficult  to  examine  the  high  degrees  of  myopia  by 
the  erect  image,,  and  by  the  inverted  image  the  enlargement  is 
sometimes  not  sufficient.  We  can  then  use  this  image  which 
the  myopic  eye  itself  produces,  by  magnifying  it;  we  make  no 
change  from  the  ordinary  way  of  examining  with  the  inverted 
image ;  it  is  only  necessary  to  move  the  lens  far  enough  away  for 
the  image  to  be  formed  between  the  lens  and  the  observed  eye. 
The  lens  then  produces  an  enlarged  virtual  image  of  this  inverted 
image,  which  is  also  inverted  and  situated  farther  behind;  to 
see  it  distinctly  it  is  often  necessary  to  place  oneself  very  near 
the  lens,  especially  if  one  uses  a  convex  glass  behind  the  mirror. 
We  can  thus  obtain  an  enlargement  nearly  as  great  as  by  the 
erect  image  (Demicheri). 

We  can  use  the  examination  by  the  inverted  image  for  the 
determination  of  the  refraction  of  the  eye,  by  measuring  the  dis- 
tance from  the  observed  eye  at  which  the  inverted  image  is 
situated,  since  this  distance  varies  with  the  refraction  of  the 
eye.  This  method,  which  was  proposed  by  Schmidt-Rimpler,  has 
never  become  very  popular. 

The  appearance  of  the  fundus  of  the  eye  is  very  nearly  the 
same  with  both  methods.  We  must  except  the  macula,  however, 
which,  by  the  inverted  image,  often  presents  itself  under  a 
special  form,  as  an  oval  spot,  with  the  long  diameter  horizontal, 
a  little  larger  than  the  papilla;  this  spot  is  dull,  a  little  darker 
than  the  rest,  and  surrounded  by  a  bright  circle,  corresponding 
to  the  convexity  of  the  border  of  the  fovea,  which  acts  as  a  kind 
of  convex  mirror.  Analogous  reflexes  often  appear  also  on 
other  parts  of  the  retina,  especially  in  young  subjects. — Differ- 
ences of  level  are  observed  by  the  parallactic  displacement  which 
is  obtained  by  subjecting  the  lens  to  a  slight  to-and-fro  move- 
ment. 

92.  Ophthalmoscopic  Examination  of  the  Refracting  Media. — 
To  examine  the  transparency  of  the  refracting  media  it  is  pre- 


246  PHYSIOLOGIC  OPTICS 

f arable  to  use  a  weak  illumination;  we  use  preferably  a  plane 
mirror  or  even  a  convex  mirror.  De  Wecker  recommended  the 
use  of  the  plates  of  Helmholtz  for  this  examination.  We  see, 
indeed,  the  shadows  which  the  opacities  produce  by  intercepting 
a  part  of  the  rays  sent  back  by  the  fundus  of  the  eye.  If  the 
fundus  is  strongly  illuminated,,  and  if  the  obstacles  are  not 
completely  opaque,  they  allow  a  part  of  the  light  to  pass  and 
the  shadow  is  less  complete. — It  is  useful  to  use  a  strong  magni- 
fying glass  for  this  examination  in  order  that  we  may  place 
ourselves  very  near  the  eye.  Otherwise  many  of  the  small 
corpuscles  may  escape  in  the  examination. 

It  is  quite  rare  for  these  opacities  to  be  visible  by  the  light 
which  they  themselves  reflect.  It  may  happen,  however,  that 
we  can  see  the  red  color  of  hemorrhages  situated  far  forward 
in  the  vitreous  body,  or  the  white  color  of  certain  opacities, 
especially  when  using  the  light  in  such  a  manner  that  it  falls 
very  obliquely  along  the  head  of  the  observer.  In  cases  of 
synchisis  scintillans  the  observing  eye  receives  light  regularly 
reflected  by  the  surfaces  of  the  small  crystals  situated  in  the 
vitreous  body. 

93.  Skiascopy. — This  method  of  examining  ocular  refraction 
was  discovered  by  Cuignei,  who  described  it  under  the  ill-chosen 
name  of  keratoscopy.  It  was  Parent  who  specially  developed 
the  method,  and  it  was  he  who  first  gave  the  correct  explanation 
of  it. 

The  observer  takes  his  place  at  one  meter  from  the  patient, 
whose  eye  he  illuminates  with  a  plane  mirror;  by  rotating  the 
mirror  around  a  vertical  axis  we  see  the  luminous  spot  on  the 
face  of  the  patient  move  in  the  same  direction.  The  illumination 
of  the  pupil  follows  the  same  direction,  whether  the  patient  be 
hypermetropic,  emmetropic  or  very  slightly  myopic. — If  the 
myopia  is  over  I  D.,  the  pupillary  light  is  displaced  in  the  con- 
trary direction,  and  if  the  myopia  is  equal  to  I  D.,  we  do  not 
see  the  light  move  in  the  pupil.  The  luminosity  diminishes  uni- 
formly in  the  entire  extent  of  the  pupil  to  disappear  suddenly. 


OPHTHALMOSCOPY 


247 


The  examination  of  figure  136  shows  that  the  retinal  image 
moves  in  the  same  direction  as  the  mirror.  If  the  observed 
person  is  hypermetropic,  emmetropic  or  myopic  less  than  I  D.,  it 


Fig.  136. — Skiascopy.     Plane  mirror. 

L,  lamp;  Mi,  first  position  of  the  mirror;  Li,  image  which  it  forms  of  the 
lamp;  Ii,  retinal  image. — Ma,  second  position  of  the  mirror;  La, 
image  of  the  lamp;  la,  retinal  image. 

is  the  erect  image  that  the  observer  sees.     The  light  seems  to 
him  to  move  on  the  retina,  as  it  really  does.    If,  on  the  contrary, 


Fig.  137. — Skiascopy.     Concave  mirror. 
The  letters  have  the  same  significance  as  in  figure  136. 

the  myopia  is  greater  than  i  D.,  he  sees  the  light  move  in  the 
contrary  direction,  because  the  light  comes  to  him  from  the  in- 


248  PHYSIOLOGIC  OPTICS 

verted  image  which  he  observes. — To  determne  the  degree  of 
ametropia,  we  place  before  the  eye  of  the  patient  stronger  and 
stronger  glasses,  until  the  shadow  covers  the  entire  pupil  at 
once;  the  patient  has  then  a  myopia  equal  to  i  D. 

If  we  use  a  concave  mirror  we  see,  as  in  the  preceding  case, 
the  luminous  spot  move  on  the  face  of  the  patient  in  the  same 
direction  as  the  mirror.  But  the  retinal  image  of  the  flame 
moves  in  a  contrary  direction:  we  see,  indeed,  on  figure  137, 
that  the  image  of  the  flame  (Lx  L2)  formed  by  the  mirror  goes 
in  a  direction  contrary  to  that  of  figure  136,  whence  it  follows 
that  it  is  the  same  for  the  retinal  image.  The  observer  also 
sees  the  ocular  glow  move  in  an  opposite  direction  if  the  ob- 
served person  is  emmetropic,  hypermetropic  or  myopic  less  than 
i  D.  and  in  the  same  direction  if  the  myopia  is  greater  than  i  D. 

Skiascopy  is  important  in  the  search  for  astigmatism  if  we 
do  not  dispose  of  it  with  an  ophthalmometer.  If  the  mirror  be 
moved  in  the  direction  of  one  of  the  principal  meridians,  every- 
thing happens  as  in  a  non-astigmatic  eye.  But  if  the  movements 
of  the  mirror  take  place  in  another  meridian,  the  shadow  is  seen 
to  move  in  a  direction  which  forms  an  angle  with  that  of  the 
mirror.  This  is  due  to  the  elliptical  form  of  the  diffusion  spot. 
If  we  draw  an  ellipse  with  oblique  axes  on  a  sheet  of  paper, 
and  observe  it  through  a  smaller  circular  aperture,  while  giving 
it  a  horizontal  movement,,  it  is  almost  impossible  not  to  give  way 
to  the  illusion  that  the  motion  takes  place  in  an  oblique  direction. 
— We  then  find  the  motion  to  give  the  mirror  in  order  that  the 
displacement  of  the  ocular  glow  takes  place  parallel  to  that  of 
the  mirror.  We  then  determine  the  refraction  of  the  principal 
meridians  in  the  ordinary  way. 

W7hen  the  ametropia  is  considerable,  the  glow  is  quite  feeble 
and  the  boundary  between  the  light  and  shade  is  curved.  If 
on  the  contrary  the  eye  is  almost  corrected,  we  see  the  glow 
very  bright  and  its  border  is  very  nearly  straight. 

The  explanation  of  this  fact,  which  has  given  rise  to  a  lively 
discussion,  is  quite  simple.  As  the  lamp  (or  its  image  formed 
by  the  mirror)  is  far  from  the  observed  eye,  there  is  formed  in 
the  emmetropic  eye  a  small  pretty  distinct  retinal  image  of  the 


OPHTHALMOSCOPY 


249 


flame  (fig.  138,  Aj).  As  all  the  light  is  concentrated  on  this 
small  image,  it  is  quite  bright  and  although  it  is  small,  it  never- 
theless fills  the  field  because  the  latter  is  also  very  small,  as 
it  is  easy  to  see  by  using  the  construction  we  have  given  for 


O 


Fig.  138. — The  thick  circle  indicates  the  limits  of  the  skiascopic  field:  A, 
in  an  emmetropic  eye;  B,  in  a  strongly  ametropic  eye.  The  square 
in  A  represents  the  image  of  the  flame;  in  B,  it  changes  into  a 
large  spot  composed  of  circles  of  diffusion. 

the  ophthalmoscopic  field.  The  right  border  of  the  ocular  glow 
corresponds  with  the  border  of  the  retinal  image  of  the  flame. 
In  the  ametropic  eye  the  field  is  large,  and  the  retinal  image  is 
displaced  by  a  diffusion  spot,  much  larger  and  consequently  not 
so  bright.  Each  point  of  the  distinct  retinal  image  is  replaced 
by  a  circle  of  diffusion  of  the  same  form  as  the  pupil  of  the 
observed  eye;  as  the  latter  is  generally  round,  the  spot  also 
takes  on  a  round  form  (fig.  138,  B)  more  pronounced  in  pro- 
portion as  the  ametropia  is  greater.  It  is  easy  to  prove  the 
exactness  of  this  explanation:  if  we  use  as  luminous  source  a 
very  long,  bright  line,  the  border  of  the  ocular  glow  remains 
straight,  even  in  the  case  of  strong  ametropia,  because  the  super- 
position of  the  circles  of  diffusion  cannot  then  produce  a  round 
form.  Likewise,  if  we  give  the  pupil  a  triangular  form,  by 
placing  a  stenopaic  opening  of  this  form  before  the  eye  of  the 
observed  person,  the  shadow  retains  also  its  rectinlinear  border, 
for  the  supposition  of  triangular  diffusion  spots  cannot  give  a 
round  form  to  the  diffusion  spot. 


250 


PHYSIOLOGIC  OPTICS 


But  in  neither  case  does  the  observer  see  a  distinct  image,  be- 
cause his  eye  is  accommodated  for  the  pupillary  plane  of  the 
observed  eye,  while  the  image  which  he  observes  is  in  front  of 
(M)  or  behind  (H)  this  plane.  And  as  it  is  not  focused  for 
the  image,  the  latter  is  seen  vaguely,  each  point  being  represented 
by  a  circle  of  diffusion,  the  border  of  which,  as  always,  corre- 
sponds with  the  border  of  the  pupil  of  the  observer. 


Patient 


Fig.  139. 


Observer 


THEORY  OF  LEROY. — The  explanation  which  Leroy  has  given 
of  skiascopy,  and  which  is  widely  accepted,  especially  in  Germany 
is  in  thorough  agreement  with  that  of  Parent  which  I  have  just 
explained.  Let  a  (fig.  139)  be  an  illuminated  point  of  the  retina 


Fig.  140. 

of  the  observed  eye,  supposed  to  be  myopic,  and  of  its  image. 
From  the  observed  eye  then  starts  the  luminous  cone  bafc,  of 
which  the  part  afmo  enters  the  observing  eye.  This  eye  sees 
luminous  the  part  of  the  pupil  which  sends  rays  to  it,  that  is 
the  part  bp,  while  pc  is  dark  because  the  rays  which  come  from 


OPHTHALMOSCOPY  251 

this  part  are  intercepted  by  the  iris  of  the  observer.  This  Leroy 
somewhat  subtly  expressed  by  saying  that  the  shadow  is  pro- 
duced by  the  iris  of  the  observer.  We  can  imagine  the  pupil  of 
the  observer  projected  through  a'  on  the  pupil  of  the  observed 
person  (fig.  140,  A)  ;  the  part  of  this  latter  which  it  would  cover 
would  appear  luminous.  In  regard  to  the  theory  of  Parent,  we 
would  say  that  the  observer  sees  the  point  a  but  dimly,  that  is 
to  say  as  a  diffusion  circle  the  border  of  which,  as  we  know, 
corresponds  to  the  border  of  the  pupil  of  the  observed  eye. 

The  two  theories  are  therefore  two  different  ways  of  saying 
the  same  thing.  But  were  the  curved  form  of  the  shadow  ex- 
plained by  the  form  of  the  pupil  of  the  observer  it  would  be 
wrong,  because  the  phenomena  do  not  change  if  the  observer 
looks  through  a  triangular  aperture  placed  in  front  of  his  pupil. 
The  form  of  the  pupil  of  the  observer  plays  no  part,  for  in 
reality  it  is  not  a  luminous  point  which  is  found  on  the  retina, 


Fig.  141. — Theory  of  the  paracentral  shadow. 

as  the  theory  of  Leroy  supposes,  but  an  image  of  the  flame  of 
which  ad  (fig.  139)  is  a  section.  The  border  of  the  image  which 
we  use  is,  therefore,  a  straight  line  perpendicular  to  the  plane 
of  the  paper,  and  it  would  be  necessary  to  repeat  the  construc- 
tion of  Leroy  for  each  point  of  this  straight  line.  We  would 
thus  obtain  a  series  of  projections  of  the  pupil  of  the  observer, 
which  would  delimit  the  part  of  the  pupil  of  the  observed  eye 
which  appears  luminous  (fig.  140,  B).  It  is  easy  to  see  that 


252  PHYSIOLOGIC  OPTICS 

the  form  of  each  diffusion  circle  has  no  influence  on  the  form 
of  the  border  of  the  shadow. 

PARACENTRAL  SHADOW. — When  one  is  near  correction,  one 
often  sees  the  shadow  move  irregularly.  Bitzos  has  described  a 
paracentral  shadow :  a  part  of  the  pupil,  near  the  center,  appears 
dark,  while  the  borders  are  still  illuminated.  This  phenomenon 
indicates  that  the  refraction  is  not  the  same  everywhere  in  the 
pupil ;  it  frequently  makes  impossible  a  very  exact  determination 
of  the  refraction. 

We  must  not,  therefore,  expect  a  very  exact  determination 
by  skiascopy,  as  is  the  case  also  for  subjective  measurement  and 
determination  by  the  erect  image,  simply  because  the  very  idea 
of  ocular  refraction  does  not  permit  of  very  great  exactness. 

Here  is  the  explanation  of  the  paracentral  shadow.  Let  us 
suppose  an  eye  emmetropic,  but  with  a  strong  spherical  aberra- 
tion so  that  the  peripheral  parts  of  the  pupil  may  be  myopic. 
The  rays  coming  from  a  luminous  point  of  the  retina  would 
then  have  the  direction  indicated  on  figure  141.  An  eye,  the 
pupil  of  which  would  be  at  P  would  receive  rays  i  and  3  and 
would  see  luminous  the  parts  corresponding  with  the  pupil, 
while  at  2  the  pupil  would  appear  dark,  since  the  ray  2  would 
not  enter  the  pupil.  The  observing  eye  would,  therefore,  see  a 
bright  center  separated  from  equally  bright  borders  by  a  dark 
ring.  If  P  be  displaced  a  little  downwards,  it  would  receive  all 
the  rays  drawn  on  the  figure,  but  some  on  the  other  half  would 
not  enter  it,  which  would  give  the  phenomenon  of  paracentral 
shadow.  This  shadow  is,  therefore,  nothing  else  than  the  mani- 
festation of  spherical  aberration.  We  have  seen  that  the  ap- 
pearance which  indicates  aberration  consists  of  a  luminous  ring 
towards  the  borders  of  the  pupil,  separated  from  the  central 
light  by  a  dark  zone;  tilting  the  mirror  slightly  the  central  light 
becomes  partly  joined  to  the  ring  and  the  dark  part  assumes  the 
form  described  by  Bitzos. 

I  have  several  times  emphasized  the  advantages  which  skia- 
scopy with  a  luminous  point  presents  for  the  study  of  optic 
anomalies  of  the  eye.  It  also  lends  itself  very  well  to  the  or- 
dinary measurement  of  refraction.  At  the  critical  moment  when 


OPHTHALMOSCOPY  253 

the  movement  of  the  light  changes  its  direction  the  far  point 
of  the  observed  eye  coincides  with  the  pupil  of  the  observer.  As, 
on  the  other  hand,  the  principle  of  Jackson  demands  that  the 
image  of  the  luminous  source  coincide  with  the  far  point  one  is 
led  to  use  a  plane  mirror  and  to  place  the  flame,  surrounded  by 
its  opaque  screen,  quite  near  the  eye  of  the  observer.  But,  in 
order  to  observe  the  luminous  band  of  astigmatism  and  the  ring 
of  aberration,  we  must  place  the  lamp  by  the  side  of  and  a  little 
behind  the  patient. 

Bibliography. — Gumming  (W.).  Medico-chirurgical  transactions.  XXIX, 
p.  284. — Briicke  (E.).  J.  Mullers  ArcMv  fur  Anatomie  und  Physiologic, 
1847,  p.  225. — Helmholtz  (H.).  Beschreibung  eines  Augenspiegels  zur 
Beobachtung  der  Netzhaut  am  lebenden  Auge.  Berlin,  1851. — Euete  (Th.). 
Der  Augenspiegel  und  das  Optometer.  Gottingen,  1852. — Coccius  (A.). 
Ueber  die  Anwendung  des  Augenspiegels,  nebst  Angdbe  eines  neuen  In- 
struments. Leipzig,  1853. — Cuignet.  Keratoscopie.  Eecueil  d'opht.,  1873- 
74. — Parent.  Diagnostic  et  determination  objective  de  l'Astigmatisme. 
Eecueil  d'opht.,  1881. — Leroy  (C.  J.  A.).  Le  phenomene  de  I'ombre 
pupillaire.  Eev.  gen.  d'opht.,  1887,  p.  289. — Bellarminoff.  Neues  Ver- 
fahren  den  AugenMntergrund  zu  besichtigen.  Miinch.  med.  Wochenschrift, 
1888. — Bitzos  (G.).  La  SMascopie.  Paris,  1892. — Demicheri  (L.). 
Exam^en  ophtalmoscopique  a  I 'image  renversee  sur  les  yeux  fortement 
myopes.  Ann.  d'oc.,  1895. 

The  theory  of  the  ophthalmoscope  is  found  explained  in  several  treatises 
on  ophthalmoscopy.  The  following  small  book  is  to  be  recommended  on 
account  of  its  brevity  and  clearness: 

Bjerrum  (I.)  (of  Copenhagen).  Instructions  pour  I'emploi  de  I'ophtal- 
moscope.  Translated  by  Grosjean.  Paris,  Steinheil,  1894. 


CHAPTER  XIV 
THE  PUPIL 

94. —  To  properly  understand  the  working  of  a  dioptric  intru- 
ment,  we  must  not  only  know  the  position  and  power  of  the 
refracting  surfaces,  but  also  the  size  and  position  of  its  dia- 
phragm. I  have  already  referred  to  the  difference  between  the 
size  and  position  of  the  apparent  pupil  and  the  real  pupil,  and 
observed  that  the  pupil  is  generally  displaced  a  little  to  the  tem- 
poral side.  Its  size  varies  in  different  people;  generally  it  di- 
minishes with  age,  and  finally  becomes  quite  small  in  old  people. 
As  a  rule  it  is  larger  in  myopes  than  in  hypermetropes,  at  least 
in  appearance,  for  the  anterior  chamber  of  myopes  is  often 
deeper,  which  makes  the  pupil  appear  larger.  In  cases  of  com- 
plete amaurosis,  the  pupil  is  immovable  and  very  large,  except 
when  the  amaurosis  has  a  spinal  origin,  in  which  case  the  pupil 
is  often  greatly  contracted. 

The  pupil  contracts  and  dilates  under  many  different  influ- 
ences; these  movements  are  very  complex  and,  for  the  most 
part,  still  imperfectly  elucidated.  All  agree  on  the  existence  of 
the  sphincter,  while  that  of  the  dilator  is  disputed,  although 
physiological  observations  make  its  existence  probable.  The 
movements  of  the  pupil  are  under  the  influence  of  the  motor 
oculi  and  the  great  sympathetic.  Cutting  the  motor  oculi  pro- 
duces a  dilatation  of  the  pupil,  much  less,  however,  than  that 
which  may  be  produced  by  atropine.  The  contractions  which  ac- 
company accommodation  and  incidence  of  light  cease  at  the  same 
time,  as  well  as  accommodation  itself.  The  contraction  which 
accompanies  incidence  of  light  is,  therefore,  produced  by  a  re- 
flex action  between  the  retina  and  the  optic  nerve  on  the  one 
hand  and  the  oculo-motor  on  the  other.  It  must  be  noted,  how- 
ever, that  Brown-Sequard  produced  a  contraction  of  the  pupil 
by  concentrating  light  on  an  enucleated  rabbit's  eye,  according 
to  which  experiment  the  light  would  also  have  a  direct  influence 

254 


THE  PUPIL  255 

on  the  muscles  of  the  iris.  An  irritation  of  the  oculo-motor  pro- 
duces a  contraction  of  the  pupil,  an  irritation  of  the  great  sym- 
pathetic at  the  neck  produces,  on  the  contrary,  a  marked  dilata- 
tion, while  the  cutting  of  this  nerve  contracts  the  pupil. 

* 
95.  Action  of  Mydriatics  and  Myotics. —  The  instillation   of   a 

drop  of  a  solution  of  atropine  (0.5  per  cent.)  produces  a  marked 
dilatation  of  the  pupil ;  it  paralyzes  its  movements  as  well  as  the 
accommodation:  the  effect  generally  lasts  eight  days.  If  we 
use  a  much-diluted  solution,  the  effect  does  not  last  so  long  and 
the  action  on  accommodation  is  much  less  pronounced.  To  ex- 
plain why  the  dilatation  by  atropine  is  much  greater  than  that  ob- 
tained by  cutting  the  motor  oculi,  it  is  supposed  that  it  acts  at  the 
same  time  by  irritating  the  terminal  fibres  of  the  great  sympa- 
thetic. 

Homatr  opine  (0.5  per  cent.)  dilates  the  pupil,  but  it  generally 
does  not  act  to  any  extent  on  the  accommodation  if  the  solution 
is  pure,  (i)  Its  effect  lasts  twenty- four  hours. 

Cocaine  (5  per  cent.)  dilates  the  pupil,  but  does  not  act  on 
the  accommodation';  at  least  I  have  not  been  able  to  find  any 
effect  on  my  own  eye.  ( i ) 

A  mixture  of  homatropine  and  cocaine  dilates  the  pupil  still 
more  than  either  one  of  these  alkaloids  by  itself  .  Such  a  mix- 
ture is  recommended,  therefore,  for  investigations  of  accommo- 
dation, the  more  so  because  the  pupil  is  dilated  some  time  be- 
fore accommodation  begins  to  diminish.  Scopolamine  ( -^  per 
cent.)  produces  complete  paralysis  of  accommodation,  with  a  very 
marked  dilatation  of  the  pupil  which  we  can  further  increase  by 
adding  cocaine. 

With  a  solution  of  eserine  (0.5  per  cent.)  we  obtain  a  very 
great  contraction  of  the  pupil,  and  the  accommodation  reaches  its 
maximum.  I  have  obtained  with  eserine  a  little  greater  ampli- 
tude than  I  could  produce  spontaneously.  It  is  doubtful  whether 
eserine  acts  directly  on  the  sphincter,  or  whether  the  contrac- 


(1)    Other   observers   maintain   the   contrary;    the    differences    are   perhaps    in- 
dividual ;  perhaps  due  to  the  fact  that  they  use  different  preparations. 


256  PHYSIOLOGIC  OPTICS 

tion  of  the  pupil  is  analogous  to  that  which  always  accompanies 
accommodation. 

96.  The  Movements  of  the  Pupil. 

i°  The  pupil  contracts  under  the  influence  of  light  (reflex  by 
the  optic  nerve).  It  is  not  alone  the  light  which  strikes  the 
retina  of  a  particular  eye,  but  also  that  which  enters  the  other 
eye,  which  causes  the  contraction.  The  pupils  are  equal  in  size, 
even  if  one  eye  is  exposed  to  a  much  stronger  light  than  the 
other.  If  the  pupil  does  not  contract  when  the  light  strikes 
the  retina  of  the  same  eye,  and  does  contract  when  it  strikes 
that  of  the  other  eye,  we  may  infer  a  complete  amaurosis  of 
the  eye  in  question.  In  complete  darkness  the  pupil  reaches 
its  maximum  dilatation,  so  that  the  iris  is  often  not  visible  (i) 
(Cohn,  Cl.  Dubois-Reymond).  This  fact  has  been  demonstrated 
by  taking  photographs  of  the  eyes  in  complete  darkness:  we 
illuminate  them  with  mixtures  of  powders,  the  light  of  which 
does  not  continue  long  enough  to  give  the  pupil  time  to  contract. 
It  is  not  easy  to  reconcile  this  observation  with  every-day  ex- 
perience, which  shows  that  the  reaction  of  the  pupil  to  light 
depends  on  the  oculo-motor,  the  cutting  of  which  produces  only 
a  medium  dilatation. 

It  is  manifest  that  the  object  of  this  contraction  of  the  pupil 
is  to  regulate  the  quantity  of  light  that  enters  the  eye. 

2°  The  pupil  contracts  during  accommodation. — To  examine 
the  functions  of  the  pupil  we  must  see  whether  it  contracts:  a) 
when  the  light  strikes  the  retina  of  the  same  eye;  b)  when  the 
light  strikes  the  retina  of  the  other  eye;  c)  when  the  patient 
makes  an  effort  of  accommodation.  We  know  that  accommoda- 
tive contraction  may  exist  without  the  reaction  to  light,  and 
vice  versa  (Argyll  Robertson).  The  accommodative  contraction 
has  this  peculiarity  that  even  the  most  peripheral  parts  of  the 
iris  show  a  centripetal  movement,  which  is  not  generally  the 
case  for  the  reaction  to  light  (Hueck). 

The  object  of  this  contraction  is  to  eliminate  the  action  of  the 


(1)  If  the  iris  is  not  visible  at  all,  it  is  an  apparent  phenomenon,  due  to 
refraction  through  the  cornea,  for  if  we  plunge  an  eye,  the  pupil  of  which  is 
dilated  to  this  extent,  in  water,  the  iris  becomes  immediately  visible  (Stadfeldt) . 


THE  PUPIL  257 

peripheral  parts  of  the  crystalline  lens,  which  do  not  sufficiently 
accommodate. 

3°  The  pupil  contracts  when  the  aqueous  humor  escapes. — I 
have  already  remarked  that  this  contraction  is  also  observed 
after  death  (Arlt},  so  that  it  must  be  considered  as  a  purely 
mechanical  phenomenon,  which  we  may  identify  with  accommo- 
dative contraction  .  I  have  made  some  experiments  to  elucidate 
the  nature  of  this  contraction;  before  describing  them  it  is  im- 
portant to  speak  of  the  posterior  chamber,  the  existence  of  which 
has  been  disputed. 

On  examining  an  eye  by  oblique  illumination,  we  easily  see 
that  the  border  of  the  iris  is  in  contact  with  the  crystalline  lens. 
We  also  see  this  very  well  by  examination  with  the  third  image 
of  Purkinje,  which  I  have  mentioned  page  50,  or  by  examining 
an  eye  affected  with  mature  cataract.  If  we  remove  the  crystal- 
line lens  from  the  eye,  or  if  it  be  dislocated,  the  iris  shows  at 
each  movement  of  the  eye  the  trembling  known  as  iridodonesis ; 
Helmholtz  and  others  were  led  to  infer  from  these  facts  the 
non-existence  of  a  posterior  chamber ;  there  exists,  nevertheless,  a 
small  space  filled  with  liquid  between  the  crystalline  lens,  the 
ciliary  body  and  the  peripheral  parts  of  the  iris.  We  sometimes 
see  in  perfect  eyes  a  slight  trembling  of  the  peripheral  parts  of 
the  iris  when  the  eye  makes  a  movement. 

The  observation  of  Arlt,  showing  that  we  still  see  the  pupillary 
contraction  after  paracentesis  has  been  performed  on  the  dead 
eye,  struck  me  forcibly.  To  verify  it  I  introduced  the  point  of 
a  Pravaz  syringe  into  the  anterior  chamber;  by  depressing  or 
withdrawing  the  piston  we  can  make  the  pupil  contract  or  dilate 
at  will.  By  removing  nearly  all  the  contents  of  the  anterior 
chamber  I  was  able  to  reduce  the  diameter  of  the  pupil  to  I  or 
2  mm.  On  the  contrary,  by  forcing  the  injection  as  far  as 
possible,  the  dilatation  may  extend  so  far  as  to  make  the  iris 
disappear,  (i)  It  is  true  that  one  part  of  the  change  is  only 
apparent,  as  Stadfeldt  has  shown:  the  more  the  pupil  recedes, 


(l)Wheu  we  increase  the  pressure  much,  the  cornea  becomes  opaque;  we  can 
make  it  almost  as  white  as  the  sclera  ;  as  soon  as  the  pressure  ceases,  it  again 
becomes  transparent. 


258  PHYSIOLOGIC  OPTICS 

the  more  enlarged  it  is  seen  through  the  cornea;  but  on  examin- 
ing the  eye  under  water,  we  find  a  very  noticeable  change.  The 
phenomenon  is  difficult  to  explain;  it  is  not  due  to  the  mere 
effect  of  pressure,  for  we  may  compress  the  eye  all  we  want  to 
without  observing  any  change  in  the  diameter  of  the  pupil;  nor 
is  it  due  to  a  difference  of  pressure  between  the  chamber  and 
the  posterior  part  of  the  globe,  for,  by  injecting  liquid  into  the 
vitreous  body  or  by  removing  it,  we  no  longer  produce  any 
change  of  the  pupil. 

I  also  injected  a  solution  of  gelatine  into  the  anterior  cham- 
ber, and  then,  by  hardening  the  eyes  slightly,  I  obtained  pretty 
fair  casts.  Under  these  circumstances  the  posterior  chamber 
is  also  always  injected;  the  cast  forms  a  prismatic  ring,  with  an 
anterior  surface  corresponding  to  the  iris,  a  posterior  surface 
corresponding  to  the  anterior  surface  of  the  crystalline  lens  and 
an  external  surface  corresponding  to  the  ciliary  body.  But, 
between  the  crystalline  lens  and  the  part  of  the  iris  next  to 
the  pupil,  we  never  find  any  gelatine,  or  if  there  is  any,  it  is  so 
thin  a  layer  that  it  is  destroyed  in  the  work  of  preparation. 

4°  During  sleep  the  pupil  is  greatly  contracted,  even  in 
amaurotic  persons,  whose  pupil  generally  is  large  and  motion- 
less. The  pupil  is  also  contracted  during  narcosis,  and  generally 
when  a  person  is  in  agony :  at  the  moment  of  death  it  is  generally 
greatly  dilated;  this  dilatation  disappears  immediately.  In  spite 
of  the  pupillary  contraction  during  sleep  the  reaction  to  light 
persists. 

5°  On  examining  the  pupil  with  a  magnifying  glass  we  observe 
rhythmic  contractions,  which,  at  least  in  part,  correspond  to 
the  systole,  and  which  are  due  to  the  fact  that  the  vessels  are 
filling  with  blood.  The  contraction  is  greater  when  the  systole 
coincides  with  an  expiration.  We  cannot  explain  in  this  way 
all  the  slight  contractions  of  the  pupil  which  are  observed  with 
a  magnifying  glass. 

6°  We  observe  a  dilatation  of  the  pupil  following  fright;  it 
also  accompanies  dyspnea,  vigorous  muscular  action  or  a  sharp 
irritation  of  any  sensitive  nerve. 


THE  PUPIL 


259 


97.  Advantage  of  the  Position  of  the  Pupil  near  the  Nodal 
Point. —  Young  remarked  that  if  the  pupil  had  been  situated 
farther  forward  in  the  eye  the  apparent  size  of  objects  would 
have  changed  every  time  we  made  an  effort  of  accommodation. 
We  have  seen  that  the  image  of  a  point  for  which  the  eye  is 
not  accommodated,  forms  a  circle  of  diffusion,  the  center  of 
which,  corresponding  to  the  middle  of  the  pupil,  is  frequently 


Fig.  142. 

brighter  on  account  of  spherical  aberration;  if  the  pupil  is  not 
too  large  we  may  consider  this  center  as  a  vague  image  of  the 
point.  Suppose  that,  in  a  state  of  repose,  the  eye  is  focused 
for  the  object  AB  (fig.  142).  The  image  of  the  point  A  is 
formed  at  Al  on  the  line  An  passing  through  the  nodal  point. 
During  accommodation  the  image  is  moved  forward  to  A2.  To 
find  the  place  where  the  diffuse  image  is  formed  on  the  retina 
we  draw  the  ray  Alp  passing  through  the  middle  of  the  pupil 
of  entrance  after  refraction,  this  ray  must  pass  through  p1  (i), 
the  middle  of  the  pupil  of  exit,  and  through  A2 ;  the  diffuse 
image  is  therefore  formed  at  A3  and  tfie  image  of  the  entire 
object  A3  B3  is  smaller  than  the  distinct  image  Al  Br  In  the 
human  eye  we  may  observe  a  slight  effect  of  this  kind  by  using 


(1)  On  the  figure  we  suppose  that  p  and  PI  coincide;  really  they  are  about  0.7 
millimeters  apart. 


260  PHYSIOLOGIC  OPTICS 

our  accommodation  while  observing  distant  objects;  it  is  more 
pronounced  when  we  replace  the  pupil  by  a  stenopaic  opening, 
at  some  distance  from  the  eye. 

The  position  of  the  pupil  near  the  nodal  point  has  probably 
still  another  advantage.  One  of  the  first  qualities  that  we  re- 
quire in  a  photographic  objective  is  that  it  be  rectilinear,  that  is 
to  say,  that  the  images  of  the  straight  lines  placed  peripherally 
in  the  field  be  straight,  and  not  curved.  We  usually  obtain  this 
effect  by  placing  the  diaphragm  in  the  nodal  plane,  and  the 
position  of  the  pupil  near  the  nodal  point  of  the  eye  seems  to 
play  a  part  for  the  correct  vision  of  objects  seen  indirectly. 

Nevertheless,  the  eye  is  not  rectilinear.  It  follows  from  a 
series  of  experiments  described  by  Helmholtz  that,  in  indirect 
vision,  the  straight  lines  appear  in  the  form  of  curves,  the  con- 
cavity of  which  is  turned  towards  the  point  fixed.  If  we  desire 
to  repeat  these  experiments,  we  must  place  ourselves  so  that 
no  other  line,  which  we  know  to  be  straight,  is  in  the  field,  for 
example  by  stooping  over  a  large  table. 

1°  We  place  on  the  table  a  small  piece  of  paper  A  (fig.  143), 
which  serves  as  a  point  of  fixation,  and  two  others,  B  and  C,  as 
far  as  possible  from  A,  without  ceasing 
to  see  them  distinctly  in  indirect  vision. 
While  fixing  A,  we  try  to  place  a  fourth 
piece,  D,  on  the  straight  line  which  joins 
B  and  C.  We  shall  nearly  always  place 
it  too  far  inwards. 

2°  If  we  place  on  the  table  a  strip  of 

0A  •«>          paper  with  parallel  borders,  8  to  10  centi- 

meters in  width,  and  fix  the  center  of  it, 
the  borders  appear  concave  towards  the 
point  of  fixation.  The  strip,  therefore, 
appears  larger  at  the  middle  than  towards 
0C  the  ends. 

Fig.  143.  3°  Guided  by  theoretical  consideration, 

the  value  of  which  may  appear  doubtful, 

Helmholtz  designed  the  hyperbolic  chess-board,  of  which  figure 
144  is  an  illustration  diminished  in  the  proportion  of  3/16.     In 


THE  PUPIL  261 

accordance  with  his  theory,  he  found  that,  placed  at  a  distance 
of  20  centimeters,  for  which  the  chess-board  was  calculated,  he 
saw  the  curves  assume  the  appearance  of  straight  lines  when 
he  fixed  the  middle.  When  he  stood  at  a  greater  distance,  the 
lines  appeared  to  have  the  curvature  which  they  really  had; 
moving  nearer  and  nearer,  he  saw  the  curvature  diminish  and 
finally  completely  disappear.  The  distance  at  which  the  curva- 
ture disappeared  was  each  time  almost  exactly  20  centimeters. 
If  he  approached  nearer  still,  the  lines  presented  the  reverse 
curvature,  appearing  concave  towards  the  middle. 


Fig.  144. — Hyperbolic  chess-board  of  Helmholtz. 

4°  Another  experiment  of  the  same  kind  consists  in  placing 
a  circular  piece  of  cardboard  in  the  periphery  of  the  visual  field ; 
above  or  below  we  see  it  elongated  in  the  horizontal  direction, 
while  on  the  two  sides  it  appears  elongate^  in  the  vertical  di- 
rection. 

We  can  express  all  these  phenomena  by  saying  that  the  visual 
field  is  seen  narrowed  towards  the  periphery.  Let  us  suppose 
the  plane  visual  field  divided  into  equidistant  zones,  and  suppose 
that  we  gave  an  illustration  of  it  by  making  the  zones  diminish 
towards  the  periphery.  We  would  thus  obtain  analogous  de- 
formities; the  straight  lines  would  be  represented  by  curves 
concave  towards  the  middle  (see  page  118).  A  circle  placed 


262  PHYSIOLOGIC  OPTICS 

peripherally  in  the  field  would  become  narrower  in  the  radial 
direction,  and  so  forth. 

To  explain  these  observations,  Helmholtz  called  attention  to 
another  observation  which  he  made,  and  which  is  itself  a  conse- 
quence of  the  law  of  Listing  (see  chapter  XIX). 

Standing  in  front  of  a  wall  we  look  at  a  point  A  situated  on  a 
level  with  the  eyes;  we  then  raise  the  look,  without  changing 
the  position  of  the  head,  towards  the  horizontal  line  which 
forms  the  upper  edge  of  the  wall.  Moving  the  look  rapidly 
along  this  line,  we  see  it  concave,  with  the  concavity  turned 
downwards  exactly  as  we  would  see  it  in  indirect  vision  by 
fixing  the  point  A,  if  it  was  sufficiently  distinct. 

Faithful  to  the  empiric  theories  by  which  he  tried  to  explain 
most  observations  on  physiologic  optics,  Helmholtz  supposed  that 
this  illusion  was  the  cause  of  the  preceding  one.  Surveying  the 
line  with  the  look  it  appears  curved  on  account  of  the  law  of 
Listing,  and  it  is  because  we  have  thus  learned  that  it  appears 
curved  that  it  does  usually  appear  so  in  indirect  vision  also. — 
We  must  note  that  this  way  of  observing  the  line,  namely  by 
surveying  it  with  the  raised  look,  appears  altogether  unusual.  I 
do  not  think  that  before  making  this  experiment  I  ever  looked 

at  a  line  in  this  way,  as  it  would  be 
more  natural  for  me  to  raise  my  head 
to.  look  at  it,  and  in  this  case  the  il- 
lusion disappears.  It  is,  therefore,  not 
easy  to  understand  how  I  would  have 
known  that  the  line  ought  to  appear 
curved. 

But  the  following  experiment  is 
still  more  at  variance  with  the  ex- 
planation in  question.  I  had  con- 
structed a  small  artificial  eye  (fig. 
145),  all  the  dimensions  of  which  ap- 
proached as  nearly  as  possible  those 
Fig7l45.  of  the  human  eye.  The  cornea  and 

Artificial  eye.  the  crystalline  lens  are  of  glass,  and 

have  the   same  curvature  as   in  the   human  eye;   in  order  to 


THE  PUPIL  263 

remedy  somewhat  the  excessive  refraction  of  the  crystalline 
lens,  I  filled  the  eye  with  a  mixture  of  glycerine  and  water, 
the  index  of  which  is  a  little  higher  than  that  of  the  vitreous 
body.  The  retina  is  replaced  by  a  hollow  hemisphere  of  ground 
glass,  having  nearly  the  curvature  of  the  retina  of  the  human 
eye.  Although  the  refraction  may  not  be  absolutely  identical 
with  that  of  the  human  eye,  the  difference,  however,  cannot  be 
very  great. 

With  this  eye  I  repeated  and  succeeded  in  all  the  experiments 
cited  above  (fig.  146).  The  image  of  the 
black  strip  has  the  borders  convex  towards  the 
periphery;  in  order  that  the  borders  of  the 
image  appear  straight  those  of  the  object  must 
be  concave.  The  image  of  a  circle  appeared 
shrunken  in  the  radial  direction,  etc.  The  ex- 
periment with  the  chess-board  of  Helmholtz 
is  still  more  conclusive.  As  long  as  the  eye  FiS-  146-  —  Image  of 


is  at  a  great  distance,  the  image  is  like  the    Tii  e  in    the 

object;  but,  according  as  we  move  the  eye 
nearer,  the  curvature  of  the  line  becomes  obliterated,  and  very 
close  to  the  drawing  the  lines  of  the  image  appear  concave  on 
the  inside.  I  tried  to  determine  the  place  where  the  direction  of 
the  curvature  changes,  or  in  other  words  the  place  where  the 
figure  appears  most  rectilinear,  and  each  time  I  found  a  distance 
of  20  centimeters,  at  least  as  exactly  as  when  making  the  experi- 
ment with  my  own  eye. 

According  to  this  experiment  it  seems  to  me  beyond  doubt 
that  all  these  deformities  depend  primarily  upon  the  form  of 
the  retina.  Projecting  a  plane  on  a  hollow  sphere,  we  necessar- 
ily obtain  towards  the  periphery  a  narrowing  of  the  projection 
analogous  to  that  which  we  have  found  for  the  eye.  It  is  possi- 
ble, however,  that  the  position  of  the  pupil  in  front  of  the  nodal 
point  may  play  a  certain  part,  for  the  illusion  appears  to  me 
rather  more  pronounced  if  I  look  through  a  stenopaic  opening, 
which  acts  as  an  artificial  pupil  placed  in  front  of  the  eye. 

This  touches  one  of  the  fundamental  questions  of  physiologic 
optics.  I  wish  to  speak  of  the  antagonism  between  the  nativistic 


264  PHYSIOLOGIC  OPTICS 

and  the  empiric  ideas.     Although  this  question  is  beyond  the 
scope  of  the  present  A\fc>rk,  I  shall  consider  it  for  a  moment. 

Looking  at  a  window,  the  visual  sense  tells  me  that  it  is  square. 
How  can  the  eye  give  this  information?  The  nativists,  among 
whom  we  must  first  mention  Bering,  say  that,  by  an  unknown 
congenital  mechanism,  the  retinal  impression  gives  directly  to 
the  mind  the  idea  of  the  form  of  the  object.  We  could  express 
this  idea  by  saying  that,  by  an  unknown  mechanism,  the  mind 
sees  the  retinal  image.  The  empiricists,  among  whom  Helmholtz 
is  the  most  celebrated,  say  that  the  retinal  image  gives  us  pri- 
marily no  information  on  the  form  of  the  object,  that  it  is  only 
a  "sign"  of  the  object,  almost  as  the  letter  A  is  the  sign  of  a 
certain  sound ;  by  the  movements  of  the  eyes  and  by  information 
furnished  by  the  touch,  we  learn  that  this  sign  is  to  tell  us  that 
the  object  is  square;  Helmholtz  expressed  his  ideas  thus:  "As 
for  me,  I  think  it  probable  that  the  figure,  form  and  position  of 
the  true  retina,  as  well  as  the  deformities  of  the  retinal  image, 
are  absolutely  unconcerned  with  vision,  provided  the  image  be 
distinct  in  its  whole  length,  and  that  the  form  of  the  retina  and 
that  of  the  image  remain  perceptibly  invariable  from  one  mo- 
ment to  another.  We  have  absolutely  no  knowledge  of  the 
existence  of  our  retina." 

Under  the  influence  of  Darwin,  an  effort  was  made  (Bonders) 
to  reconcile  the  two  schools  by  saying  that  the  qualities  in  ques- 
tion are  the  result  of  experiences,  not  of  the  individual,  but  of 
the  species.  Understood  in  this  sense  the  empiric  ideas  scarcely 
differ  from  the  nativistic  ideas,  the  qualities  being  then  con- 
genital in  the  same  sense  as,  for  example,  the  actual  form  of 
our  organs,  and  we  would  then  have  to  distinguish  sharply  be- 
tween what  we  may  suppose  learned  by  the  same  individual  and 
what  is  due  to  the  experience  of  the  species. 

The  empiric  theories  are  more  attractive  because  they  make 
an  attempt  at  explanation,  while  the  nativistic  theories  exclude 
all  hope.  But  it  would  be  necessary  to  apply  them  only  to  the 
phenomena  for  which  they  readily  adapt  themselves,  and  it 
seems  to  me  that  the  great  physicist  of  Berlin  has  gone  too  far 
in  being  willing  to  deny  the  relation  between  the  illusions  here 


THE  PUPIL  265 

described  and  the  deformities  of  the  retinal  image.  It  seems 
to  me  that  there  must  exist  a  mechanism  by  which  we  can  ac- 
count for  the  existence  of  these  deformities. 

Bibliography. — The  opposition  to  the  too  free  application  of  empiric 
ideas  does  not  date  from  yesterday.  See  GEuvres  de  Young,  p.  239.  "We 
are  certainly  obliged  every  moment  to  call  experience  to  our  aid  in  order 
to  correct  the  errors  of  one  of  the  senses  by  comparison  with  the  per- 
ceptions of  the  others.  [But]  it  seems  to  me  that  some  scientists  go  too 
far  when  they  assert  that  the  use  of  all  our  senses  is  derived  from  experi- 
ence alone  without  being  willing  to  admit  the  existence  of  an  instinct  on 
a  par  with  it,"  etc. 

Arlt  (F.).  Zur  Anatomic  des  Auges.  Arch.  f.  Ophth.  Ill,  2. — Du  Bois- 
Reymond  (Cl.).  Ueber  Photographien  der  Augen  ~bei  Magnesiumblitz. 
Arch.  f.  Physiologic,  1888,  p.  394. — Tscherning  (M.).  La  contraction  de 
I'iris  accompagnant  I'ecoulem&nt  de  I'humeur  aqueuse.  Bull,  de  la  Soc. 
franc,  d'opht.,  1885,  p.  305. — Tscherning  (M.).  Quelques  consequences 
de  la  loi  de  Listing.  Ann.  d'oc.,  Sept.,  1888. — Tscherning  (M.).  La 
deformation  des  dbjets  vus  indirectement.  Bull,  de  le  Soc.  franc,  d'opht., 
1895,  p.  403. 


BOOK  II 

FUNCTIONS  OF  THE  RETINA 


CHAPTER   XV 

CHANGES  WHICH  THE  RETINA  UNDERGOES 

UNDER  THE  INFLUENCE  OF  LIGHT 

98. —  The  sensitive  layer  of  the  retina  is,  in  all  probability, 
that  with  the  cones  and  rods.  Besides  the  fact  that  the  very 
structure  of  the  layer  makes  this  hypothesis  probable,  it  is  fur- 
ther strengthened  by  the  experiments  and  measurements  of  H. 
Muller  (on  the  entoptic  vision  of  the  vessels,  see  page  186)  as 
well  as  by  observations  on  visual  acuity.  But  we  have  not  suc- 
ceeded in  explaining  in  a  satisfactory  manner  the  mechanism 
by  which  light  is  transformed  into  nervous  action.  We  have 
succeeded  in  proving  a  certain  number  of  changes  which  the 
retina  undergoes  under  the  influence  of  light,  and  we  have 
studied  on  the  other  hand  the  functions  of  the  retina,  which  are 
now  very  well  known,  but  we  have  not  succeeded  in  explaining 
their  mutual  relations. 

RETINAL  PURPLE. — If  we  examine  the  eye  of  an  animal  which 
has  been  left  in  darkness  for  some  time  before  enucleation,  we 
find  that  the  external  segment  of  the  rods  has  a  purple  color 
which  disappears  very  quickly  under  the  influence  of  daylight, 
passing  through  a  yellow  tint.  The  cones  have  not  this  colora- 
tion and  the  fovea  of  the  human  eye,  which  is  composed  of 
cones  only,  is  without  color.  If  we  expose  the  eye  of  a  living 
rabbit  to  daylight  for  a  quarter  of  an  hour,  the  purple  first 
changes  to  a  yellow  and  then  completely  fades  away.  Placing 
it  so  that  the  image  of  a  bright  object,  a  window  for  example, 
may  be  formed  on  the  retina,  we  can  thus  obtain  a  permanent 
image  (optogram).  If,  after  having  caused  the  purple  to  fade 
away,  we  leave  the  animal  in  darkness,  the  purple  color  returns 
gradually,  provided  that  the  retina  be  in  contact  with  the  pig- 

266 


CHANGES  WHICH  THE  RETINA  UNDERGOES  267 

ment  cells.  It  is  not  necessary  that  they  be  the  pigment  cells 
of  the  same  animal:  if  we  place  the  retina  of  one  eye  in  the 
place  of  that  of  another  eye  the  reproduction  of  the  purple  is 
also  effected  in  darkness. 

Vision  does  not  depend  on  the  retinal  purple,  since  there  is 
no  purple  in  the  fovea,  since  rabbits  whose  retinae  we  have  al- 
lowed to  fade  away  completely  are  not  blind,  and  since  there 
are  certain  classes  of  animals,  serpents  for  example,  in  which 
the  purple  is  wanting. 

The  retinal  purple  was  discovered  by  Boll  in  1876;  subse- 
quently Kuehne  labored  much  with  the  question,  studying  es- 
pecially the  chemical  properties  of  the  retinal  purple  and  yellow. 
The  enthusiasm  with  which  the  discovery  of  Boll  was  first  re- 
ceived quickly  grew  cold  when  it  was  seen  that  it  did  not  give 
a  direct  explanation  of  the  mechanism  of  vision.  Some  time 
ago  the  question  was  again  taken  up  and  an  effort  made  to 
put  the  retinal  purple  in  relation,  on  the  one  hand,  with  the 
vision  of  certain  colors,  on  the  other  with  the  adaptation  of  the 
retina  to  very  feeble  light.  These  efforts,  some  of  which  will  be 
mentioned  later  on,  have,  up  to  the  present,  only  a  hypothetic 
character. 

99.  Movements  of  the  Pigment  under  the  Influence  of  Light. — 

By  experimenting  with  frogs,  Boll  observed  yet  another  phe- 
nomenon dependent  on  the  influence  of  light.  He  observed  that 
it  was  easy  to  separate  the  retina  from  the  epithelium  when  the 
animals  are  left  in  darkness  for  an  hour  or  two  before  death. 
If  the  animal  has  been  exposed  to  light  for  a  certain  period 
before  enucleation  it  is,  on  the  contrary,  difficult  to  separate 
them,  and  if  we  sever  the  retina  we  find  it  covered  with  black 
pigment  spots  which  adhere  to  it.  We  know  that  the  epithelial 
cells  send  prolongations  between  the  rods  which  they  separate 
from  one  another.  In  darkness  the  pigment  is  found  massed 
between  the  exterior  segments  of  the  rods,  but  under  the  in- 
fluence of  light  it  is  displaced  so  as  to  cover  the  terminal  surface 
of  the  rod,  and  is  projected  among  the  rods,  sometimes  even 
to  the  external  limiting  membrane.  The  external  segment  of 


268 


PHYSIOLOGIC  OPTICS 


the  rod  is  swollen  at  the  same  time.  Analogous  phenomena  have 
been  described  in  the  eyes  of  birds,  mammals,  and  also  in  a 
human  eye. 

Fan  Gender  en  Stort  made  a  step  in  advance  in  the  biology  of 
the  retina  by  using  a  method  by  which  the  retina  is  hardened  in 
a  very  little  while  (nitric  acid)  ;  instead  of  cutting  the  retina 
with  a  microtome  he  hacked  it  with  a  razor.  He  showed  that  there 
is  yet  another  change  which  the  retina  undergoes  when  exposed 
to  light.  In  an  animal  left  in  darkness  some  time  before  death, 
we  find  the  internal  part  of  the  cones  long  and  filiform,  and  the 
length  differs  for  different  cones  so  that  the  latter  are  arranged 
in  several  rows  quite  a  distance  from  the  limitans  externa.  If, 
on  the  contrary,  the  animal  has  been  exposed  to  light,  the  internal 
part  of  the  cones  is  shortened  and  swollen:  all  the  cones  are 


A  B 

Fig.  146a. — Section  of  the  retina  of  a  frog.     After  Van  Genderen.  Stort. 
A,  in  darkness;  B,  in  light. 

placed  in  a  row  along  the  limitans  externa  (fig.  1460).  Accord- 
ing to  Van  Genderen  Stort  the  retinal  purple  is  also  in  the  cells 
of  the  pigment  epithelium,  and  it  is  probably  secreted  by  these 
cells.  He  thinks  that  the  pigment  displacement  has  for  its  object 


CHANGES  WHICH  THE  RETINA  UNDERGOES  269 

the  protection  of  the  rods  against  light,  and  that  it  is  due  to  this 
fact  that  the  epithelial  cells  send,  under  the  influence  of  light, 
prolongations  between  the  rods,  almost  like  the  cells,  called  chro- 
matophres,  which  make  the  skin  of  some  lower  animals  change 
color  under  the  influence  of  light.  Van  Genderen  Stort  was  kind 
enough  to  make  a  present  of  some  of  his  beautiful  preparations 
to  our  laboratory.  The  phenomena  are  so  distinct  that  the  first 
glance  at  the  preparation  enables  one  to  tell  whether  the  animal 
was  exposed  to  light  or  not. 

We  must  note  further  that  Kuehne  observed  certain  galvanic 
phenomena  dependent  on  the  action  of  light  on  the  retina. 

Bibliography. — Boll  (F.).  Du  Bois-Reymonds.  Archiv.  f.  Anat.  u. 
PhysioL,  1877,  p.  4. — Boll  (F.).  Monatsber.  de.  Akad.  Berlin,  1877,  Jan. 
11. — Kuehne  (W.),  in  Hermann  (L.)  Handbuch  der  Physiologic.  Leip- 
zig, 1879. — Van  Genderen  Stort.  Acad.  d' Amsterdam,  June  28,  1884. 


CHAPTER   XVI 

THE  LIGHT  SENSE 

The  functions  of  the  retina  are  divided  into  three  classes:  the 
light  sense,  the  color  sense,  and  the  form  seme. 

The  light  sense  is  the  faculty  of  recognizing  the  different  lu- 
minous intensities. 

100.  Psychophysical  Law  of  Fechner. — According  to  this  law 
the  smallest  difference  of  perceptible  illumination  is  a  constant 
fraction  (about  i  per  cent.)  of  the  total  illumination. 

Fechner  came  to  formulate  his  law  by  the  following  observa- 
tions. One  day  he  found  a  scarcely  perceptible  difference  of 
brightness  between  two  clouds,  and  was  much  surprised  to  see 
this  difference  persist  on  looking  through  a  quite  dark  smoked 
glass.  He  calls  this  law  psycho  physical  because,  rinding  it  also  for 
other  senses,  he  was  led  to  consider  it  as  a  general  law  of  per- 
ception. If,  for  example,  a  line  must  have  a  length  of  105  milli- 
meters in  orcler  that  we  can  tell  with  certainty  that  it  is  longer 
than  another  of  100  millimeters,  we  will  also  find  that  a  line 
must  be  at  least  210  millimeters  for  us  to  be  able  to  tell  with 
certainty  that  it  is  longer  than  another  of  200  millimeters.  In 
both  cases  the  relation  between  the  smallest  perceptible  differ- 
ence and  the  total  length  is  the  same,  one-twentieth.  It  is  so  also 
if  we  examine  the  smallest  perceptible  difference  between  two 
weights,  and  so  with  the  other  senses. 

We  notice  that  our  senses  differ  in  this  respect  from  most  of 
our  instruments.  With  an  ordinary  double  decimeter,  the  shortest 
distance  that  we  can  measure  (I  do  not  say  estimate)  is  a  half- 
millimeter;  the  smallest  measurable  difference  between  two  lines 
would  be,  therefore,  a  half-millimeter,  and  this  whatever  may 
be  the  length  of  the  lines  to  be  measured. 

To  determine  the  ratio  between  the  smallest  difference  of  per- 
ceptible illumination  and  the  toal  illumination,  Fechner  used  the 

270 


THE  LIGHT  SENSE  271 

following  experiment  which  had  already  been  described  in  the 
middle  of  the  last  century  by  Bouguer  and  by  Lambert.  The 
former  had  also  observed  the  fact  on  which  Fechner  later  based 
his  law. 

i°  Let  us  place  at  some  distance  from  a  screen  two  candles, 
A  and  B  (fig.  147),  of  equal  intensity  I,  and  place  between  the 
candles  and  the  screen  a  stick  so  that  it  forms  two  shadows  a 
and  b  on  the  screen.  The  shadow  a  is  formed  by  A,  and  conse- 
quently illuminated  only  by  B;  the  shadow  b  receives  light  only 


Fig.  147. — Experiment  of  Bouguer. 

from  A,  and  the  remainder  of  the  screen  receives  light  simultan- 
eously from  B  and  A.  By  moving  B  away  from  the  screen,  the 
shadow  b  becomes  weaker  and  weaker,  and  when  the  distance 
of  B  from  the  screen  is  nearly  ten  times  that  of  A  it  ceases  to 
be  visible. 

2°  We  replace  the  candles  by  others  of  one-half  less  intensity, 
and  repeat  the  experiment :  we  find,  as  in  the  preceding  case,  that 
the  shadow  ceases  to  be  visible  at  the  moment  when  the  distance 
of  B  from  the  screen  is  about  ten  times  that  of  A. — And  we 
shall  find  the  same  result,  whatever  may  be  the  intensity  of  the 
candles. — The  law  of  Fechner  is  thus  verified. 

Suppose  that,  in  case  of  i°,  at  the  moment  when  the  shadow 
disappears,  B  is  at  500  centimeters  from  the  screen,  A  at  50 
centimeters.  We  know  that  the  illumination  is  proportional  to 
the  intensity  of  the  luminous  source,  and  inversely  proportional 
to  the  square  of  the  distance.  A  gives,  therefore,  to  the  screen 
an  illumination  of  —  ,  B  an  illumination  of  _L ,  while  the  shadow 


272  PHYSIOLOGIC  OPTICS 

b  receives  an  illumination  of  _L  only.    The  difference  between  the 
illumination  of  the  screen  and  that  of  the  shadow  is  therefore : 


-L     JLA     _L     _L_ 

502  +  5002/  ~502~  5002 


and  the  ratio  between  this  difference  and  the  illumination  of  the 
screen  is 


5002 


502  5002 


102  -f  1          101 


or  T-J-Q-,  since  the  measurement  is  not  very  exact. 
In  case  2°  the  relation  is 

1/2  I 


5002 


1/21   ,    1/21      ~  101 
502  5002 

It  is  consequently  the  same  in  both  cases. 

The  law  of  Fechner  explains  many  of  the  phenomena  daily 
observed. — If,  after  having  performed  with  the  candles  the  ex- 
periment cited  above,  we  open  the  shutters  so  that  the  daylight 
strikes  the  screen,  the  shadows  disappear.  The  difference  be- 
tween the  illumination  of  the  shadow  and  that  of  the  screen  re- 
mains the  same,  but  the  ratio  between  this  difference  and  the 
total  illumination  of  the  screen  is  much  below  the  fraction  of 
Fechner. — We  read  as  well  in  the  evening,  with  a  gas  light, 
as  in  day  time,  although  the  illumination  in  day  time  is  enorm- 
ously more  powerful,  because  the  ratio  between  the  light  re- 
flected by  the  black  letters  and  that  reflected  by  the  white  paper 
remains  the  same. — In  a  space  illuminated  by  a  very  powerful 
lamp,  the  flame  of  a  candle  held  at  some  distance  from  the  screen 
produces  a  shadow  of  it,  because  it  absorbs  a  part  of  the  light 
of  the  lamp.  If  we  move  the  candle  nearer  the  screen,  the  illu- 
mination increases  and  the  shadow  disappears,  although  the  dif- 
ference of  brightness  between  it  and  the  background  remains 
the  same. 


THE  LIGHT  SENSE  273 

The  law  of  Fechner  is  true  only  for  medium  degrees  of  illumi- 
nation. If  the  illumination  becomes  very  feeble,  the  difference 
must  be  relatively  much  more  considerable.  We  read  very  well 
with  a  gas  light;  but  if  we  lower  the  flame  much  we  cannot  read 
any  longer,  although  the  ratio  between  the  light  reflected  by  the 
letters  and  that  reflected  by  the  paper  remains  the  same. — It  is 
possible  that  this  difference  may  be  due  to  what  is  called  the 
retina's  own  light,  an  expression  by  which  we  designate  the 
feeble  glow  which  may  still  be  perceived  in  a  completely  dark 
room,  and  which  is  due  to  internal  causes  (friction  of  the  blood 
in  the  vessels  of  the  retina  against  the  sensitive  layer,  perhaps 
also  processes  in  certain  parts  of  the  brain,  etc.).  Wfe  can  con- 
ceive that,  if  this  light  is  added  to  that  reflected  by  the  printed 
sheet,  the  difference  of  brightness  between  the  letters  and  the 
white  sheet  may  fall  below  the  limit  of  Fechner. — The  law  of 
Fechner  also  ceases  to  be  applicable  when  the  light  is  very  strong. 
This  is  why  we  cannot  see  the  spots  on  the  sun  with  the  naked 
eye,  on  account  of  the  dazzling,  but  very  well  with  a  smoked  glass. 

But,  within  the  very  extended  limits  which  correspond  almost 
to  the  limits  of  illumination  which  we  use,  the  law  of  Fechner 
is  verified  with  very  great  exactness.  It  is  not  absolute,  how- 


0* 

...... 

j 

N\% 

f 

\ 

t 

\ 

! 

\ 

} 

: 

\ 

Fig.  148. 

ever :  in  order  to  distinguish  very  fine  shades,  it  seems  that  there 
is  a  certain  illumination  which  is  most  favorable,  viz.,  that  which 
approaches  the  light  of  a  clear  day. 

The  acuity  of  the  light  sense  may  be  expressed  by  the  inverse 
of  the  fraction  of  Fechner.  If  the  latter  be  _*_  ,we  say  that  the 
acuity  of  the  luminous  sense  is  equal  to  100;  if,  by  greatly 


274  PHYSIOLOGIC  OPTICS 

diminishing  the  illumination,  the  fraction  rises  to  JL  we  say 
that  the  acuity  is  only  50,  and  so  forth. 

We  could  illustrate  the  relation  between  the  light  sense  and 
the  illumination  by  a  curve  which  would  have  a  form  like  that 
of  figure  148.  The  division  of  the  horizontal  line  would  indicate 
the  degree  of  illumination,  beginning  on  the  left  by  complete 
darkness,  and  terminating  on  the  right  by  the  light  of  the  sun. 
The  ordinate  of  each  point  of  the  curve  would  measure  the 
acuity  of  the  light  sense.  Ais  long  as  the  illumination  is  very 
weak,  the  eye  sees  nothing:  when  it  reaches  a  certain  degree 
which,  in  the  figure,  is  marked  by  the  letter  a,  the  eye  begins  to 
be  able  to  distinguish  white  objects.  This  degree  of  illumina- 
tion, which  forms  the  lowest  limit  of  visibility,  is  called  threshold 
("Reizschwelle").  As  long  as  the  illumination  remains  so  feeble, 
the  light  sense  is  not  very  acute;  the  perceptible  differences  are 
considerable.  But  the  acuity  increases  quickly,  and  when  the  il- 
lumination has  reached  a  certain  degree,  b,  the  acuity  reaches 
the  degree  which  it  holds  for  a  long  time,  until  the  illumination 
has  attained  the  power  c.  It  is  for  the  part  be  that  the  law  of 
Fechner  is  true,  but  not  exactly,  for  this  part  of  the  curve  is 
not  altogether  straight.  It  reaches  its  highest  point  at  M. 

If  we  increase  the  light  still  more,  the  luminous  sense  falls 
quickly;  there  is  again  need  of  very  considerable  differences  of 
light  in  order  that  the  differences  may  be  distinguished. 

Let  us  designate  by  a  the  smallest  difference  of  appreciable 
sensation.  If  a  light  of  a  certain  intensity  I  produces  a  certain 
sensation  S,  there  is  need  of  an  intensity  1+^01=-^;  I  to  pro- 
duce the  sensation  S+a,  an  intensity  of  ^1 1  +  J^1  x  —  =  I  (^)2 
to  produce  the  sensation  S+2a,  an  intensity  of  I  (  — )3  to  pro- 
duce the  sensation  S-f-3fl,  and  so  forth.  It  is  under  this  form 
that  the  law  was  promulgated  by  Fechner,  for  the  fact  itself  was 
known  since  the  works  of  Bouguer  at  the  commencement  of  the 
eighteenth  century.  The  right  by  which  we  make  the  differences 
designated  by  a  equal  to  one  another  may  be  disputed. 

101.  Measurement  of  the  Light  Sense. — We  usually  limit  our- 
selves to  determining: 


THE  LIGHT  SENSE  275 

i  °  The  threshold,  the  lowest  limit  at  which  the  eye  begins  to 
distinguish  anything  (corresponding  to  the  point  a  of  the  curve)  ; 
2°  The  least  difference  of  brightness  which  we  can  distin- 
guish by  ordinary  illumination,  corresponding  to  B&  or  to  Mm 
(fig.  148).  It  is  this  determination  which  we  have  just  made 
with  the  candles. 

We  determine  the  threshold  (i)  with  the  photoptometer  of 
Foerster  (fig.  149).  It  is  a  box  painted  black  inside.  The  pa- 
tient looks  through  two 
apertures,  correspond- 
ing to  his  eyes  a  and 
a1?  towards  a  white 
surface,  placed  at  the 
far  end  of  the  box,  on 
which  are  traced  large 
black  marks  T.  The 
^_  only  light  which  can 

•  *^  penetrate  into  the  box 

Fig.  149.  . 

comes   from   a   square 

window  F,  the  aperture  of  which  we  can  change  and  which  is 
placed  beside  the  apertures  through  which  the  patient  looks. 
Behind  the  window,  which  is  covered  with  oil  paper,  burns  a 
standard  candle  L.  The  minimum  aperture  of  the  window  per- 
mitting the  patient  to  see  the  black  marks  gives  the  threshold. 
The  test  is  not  very  exact;  it  is  difficult  to  obtain  very  uniform 
answers,  and  adaptation  enormously  influences  the  result. 

The  photoptometer  of  Charpentier,  also  intended  to  determine 
the  threshold,  consists  of  a  tube,  22  cm.  long  and  5  cm.  wide, 
the  extremities  of  which  are  closed  by  plates  of  ground  glass  A 
and  B.  At  the  middle  of  the  tube  are  placed  two  lenses  of 
ii  cm.  focal  distance,  and  between  them  a  diaphragm  with 
changeable  aperture.  On  illuminating  the  plate  A  the  lenses 
project  an  image  of  it  on  the  plate  B,  the  brightness  of  which 


(1)  It  is  doubtful  whether  the  determination  of  the  threshold;  is  really  any- 
thing else  than  the  determination  of  the  fraction  of  Fechner  for  a  very  weak 
illumination. — Theoretically,  for  the  determination  of  the  threshold,  it  ought 
to  be  required  that  the  eye  can  compare  a  very  weak  light  with  absolute  black  ; 
but  we  cannot  produce  absolute  black  on  account  of  the  retina's  own  light. 


276 


PHYSIOLOGIC  OPTICS 


image  we  may  cause  to  change  by  changing  the  aperture  of  the 
diaphragm.  It  is  the  plate  B  which  serves  for  the  observation; 
for  the  protection  of  the  eye  of  the  observer  we  may  add  to 
it  a  second  tube  blackened  internally,  the  length  of  which  cor- 
responds to  the  distance  for  work  of  the  observer.  An  eye- 
shade  which  permits  of  exact  adaptation  to  the  borders  of  the 
orbit  excludes  all  extraneous  light.  The  minimum  aperture  of 
the  diaphragm  which  permits  the  observer  to  distinguish  the 
plate  B,,  determines  the  threshold. — In  every  instrument  of  this 
kind  the  difficulty  consists  especially  in  finding  a  luminous  source 
which  can  give  a  constant  and  uniform  illumination. 

In  order  to  determine  the  smallest  perceptible  difference  we 
can  use  the  method  with  the  candles,  described  above.    Another 


Fig.  150. — Disc  of  Masson. 

method  consists  in  the  use  of  the  disc  of  Masson,  a  white  disc  of 
which  sectors  of  different  sizes  have  been  blackened  (fig.  150). 
By  subjecting  this  disc  to  a  sufficiently  rapid  rotation,  we  see 
three  gray  rings  separated  by  white  intervals.  Supposing  that 
the  sector  a  is  20°,  the  sector  b  10°  and  the  sector  c  5°,  and 
supposing,  which  is  not  strictly  true,  that  the  black  does  not 
reflect  any  light  at  all,  the  brightness  of  the  three  gray  rings 
would  be  340,  350  and  355,  if  we  place  the  light  of  the  white 


THE  LIGHT  SENSE 


277 


rings  at  360.  The  difference  between  the  exterior  gray  rings 
and  the  white  will  be  5,  and  the  relation  between  this  difference 
and  the  white  will  be  A—  _L,  which  represents  the  value  of 
the  fraction  of  Fechner  of  the  examined  subject,  if  he  can  dis- 
tinguish the  three  images.  If  he  can  distinguish  only  two,  the 
fraction  of  Fechner  is  360~  350=.L,  and  so  forth.  A  great  num- 

360  36 ' 

ber  of  rings  must  be  used;  the  illumination  must  be  good,  and 
the  patient  must  not  be  too  far  away,  in  order  to  eliminate  the 
influence  of  a  diminished  visual  acuity.  It  is  evident,  however, 
that  we  cannot  completely  eliminate  it;  the  acuity  may  be  so 
poor  as  to  prevent  the  patient  from  distinguishing  anything. 

To  obtain  an  impression  of  a  uniform  gray  with  the  disc  of 
Masson,  it  is  necessary  that  it  rotate  with  a  certain  speed,  about 
20  to  30  times  per  second.  If  the  disc  carries  several  black  and 
white  sectors,  alternating,  the  speed  may  be  less.  In  case  the 
speed  is  not  sufficient,  the  disc  gives  a  scintillating  impression 


Fig.  150a. — A,  Disc  of  Helmholtz;  B.  Disc  of  Benham. 

and  we  often  observe  on  it  very  beautiful  colors.  The  disc  A 
(fig.  1500)  has  been  described  by  Helmholtz:  with  a  certain 
speed  the  external  ring  shows  very  vivid  colors,  among  which 
the  red  and  green  predominate;  they  are  often  arranged  in  a 
manner  which  recalls  a  series  of  short  spectra,  as  we  observe 
them  with  gratings.  But  the  phenomena  are  very  changeable ;  in 
the  second  ring,  which  has  only  four  sectors,  the  yellow  and  blue 
predominate  with  this  speed,  but  only  to  a  slight  extent.  If  we 


278  PHYSIOLOGIC  OPTICS 

increase  the  speed  the  external  ring  gives  a  uniform  gray,  while 
the  second  ring  assumes  the  appearance  which  the  external  ring 
had  previously.  In  figure  i$oa,  B  represents  the  disc  of  Benham. 
If  we  make  it  rotate  in  the  direction  of  the  arrow,  the  arcs  form 
concentric  circles  which  present  quite  vivid  colors  in  the  follow- 
ing order,  starting  from  the  middle:  red,  brown,  olive-green, 
blue.  Making  the  disc  rotate  in  the  opposite  direction,  the  order 
of  the  colors  is  reversed.  The  most  beautiful  of  the  colors  is 
the  red;  the  circles  seem  traced  in  blood. 

The  nature  of  these  phenomena  is  not  yet  elucidated.  We 
must  not  think  that  it  is  due  to  a  decomposition  of  the  white 
light,  for  the  experiment  succeeds  perfectly  when  illuminating 
the  disc  with  homogenous  light,  providing  it  is  sufficiently  strong 
We  even  see  colors  of  this  kind  when  looking  towards  the  homo- 
genous sodium  flame. 

Another  method  of  studying  the  power  of  distinguishing  differ- 
ences of  brightness  consists  in  examining  the  visual  acuity  for 
pale  letters,  the  brightness  of  which  we  can  determine  by  com- 
paring them  with  the  rings  on  the  disc  of  Mass  on.  This  method, 
which  was  described  by  Javal,  was  later  developed  by  Bjerrum. 
It  would  be  better  to  have  a  series  of  tables  of  visual  acuity 
with  paler  and  paler  letters,  but  generally  one  suffices;  Bjerrum 
recommended  the  use  of  letters,  the  brightness  of  which  is  one- 
twelfth  weaker  than  that  of  the  background.  For  these  letters, 
a  normal  individual  has  an  acuity  of  about  one-third  the  acuity 
which  he  has  for  black  letters  on  a  white  ground.  It  is  evident 
that  this  method  cannot  be  considered  as  an  exact  measure  of 
the  light  sense,  since  the  visual  acuity  plays  a  great  part  in  the 
response  of  the  patient.  In  order  to  eliminate  to  a  certain  ex- 
tent this  influence,  one  can  use  one's  own  eye  as  a  control,  by 
lowering  his  visual  acuity  by  means  of  a  convex  glass,  until  it 
is  equal  to  that  of  the  patient. 

102.  Results. —  The  threshold  of  the  normal  eye  was  deter- 
mined by  Aubert.  He  found  that  the  weakest  light  that  we 
can  distinguish  is  that  of  a  sheet  of  white  paper  illuminated  by 
a  candle  placed  at  a  distance  of  from  200  to  250  meters.  The 


THE  LIGHT  SENSE  279 

threshold  varies  much  with  the  state  of  adaptation  of  the  eye ; 
placed  in  a  dark  room,  we  do  not  at  first  distinguish  objects 
which  we  see  very  distinctly  later  on  when  accustomed  to  the 
darkness.  For  the  determination  of  the  threshold  it  is,  there- 
fore, necessary  to  leave  the  patient  some  time  (as  much  as  20 
minutes)  in  the  darkness,  with  eye  bandaged,  before  beginning 
the  examination.  It  seems  that,  by  this  stay  in  the  darkness, 
the  entire  curve  (fig.  148)  is  displaced  towards  the  left,  and 
also  to  its  extreme  limit,  for  on  leaving  the  darkness  the  eye  is 
dazzled  by  an  illumination  which  it  usually  bears  very  well. 

The  fraction  of  Fechner  varies  in  normal  persons  between  _L 
and  _L_  (0.55  to  i  per  cent.). 

180 

For  a  very  weak  illumination,  the  light  sense  of  the  macula 
is  less  acute  than  that  of  the  surrounding  parts;  by  fixing  a 
point  a  little  to  one  side  of  it,  we  better  distinguish  objects  the 
brightness  of  which  differs  only  slightly  from  that  of  the  back- 
ground, for  example,  when  we  try  to  distinguish  very  dim  stars. 
According  to  certain  authors,  Parinaud  for  instance,  this  phe- 
nomenon must  be  attributed  to  the  fact  that  the  fovea  does  not 
possess  the  faculty  of  being  able  to  adapt  itself  to  very  weak 
illuminations  like  the  rest  of  the  retina,  and  this  difference  is 
explained,  because  the  fovea,  composed  of  cones,  has  no  retinal 
purple,  which  is  considered  as  the  organ  of  adaptation.  This 
hypothesis  is  confirmed  by  another  fact,  namely,  the  knowledge 
that  the  time  of  repose  which  the  eye  requires  to  reach  complete 
adaptation  is  nearly  the  same  (about  20  minutes)  as  that  which 
is  necessary  for  the  reproduction  of  the  purple.  It  is  possible, 
however,  that  the  inferiority  of  the  macula  may  be  partly  due 
to  its  yellow  pigmentation.  The  pigment  absorbs  a  part  of  the 
blue  rays,  which,  as  we  shall  see,  play  a  dominant  part  in  vision 
by  weak  illuminations. 

The  threshold  is  displaced  upwards  in  patients  suffering  from 
hemeralopia.  It  seems,  however,  that,  in  many  cases,  there  is 
question  rather  of  an  anomaly  of  the  adaptation,  which  requires 
much  more  time  to  take  place  than  in  the  normal  eye.  Leaving 
a  person  affected  with  hemeralopia  in  darkness,,  he  continues  to 
improve  for  some  time.  We  can  prove  the  existence  of  hemera- 


280  PHYSIOLOGIC  OPTICS 

lopia  with  the  photoptometer  of  Foerster,  or  by  examining  the 
visual  acuity  while  we  lessen  the  illumination.  Hemeralopia  is 
a  constant  symptom  of  pigmentary  retinitis ;  we  meet  it  as  often 
in  cases  of  syphilitic  retino-choroiditis,  sometimes  in  cases  of 
detachment  of  the  retina  or  in  glaucoma.  It  is  extremely  rare 
in  cases  of  pure  atrophy  of  the  optic  nerve.  In  cases  of  idio- 
pathic  hemeralopia,  we  find  nothing  in  the  fundus  of  the  eye; 
this  disease  is  often  congenital  and  hereditary,  and  therefore 
incurable;  if,  on  the  contrary,  the  disease  has  existed  only  for  a 
short  time,  its  prognosis  is  favorable;  it  sometimes  has  an  en- 
demic character.  It  may  happen  that  the  peripheral  part  of  the 
visual  field  only  is  affected;  we  then  establish  the  existence  of 
the  disease  by  examining  the  visual  field  with  a  weak  illumina- 
tion. 

We  sometimes  meet  cases  in  which  the  fraction  of  Fechner  is 
increased ;  in  which,  consequently,  the  patients  cannot  distinguish 
gray  from  white.  This  affection  is  met  with  especially  in  cases 
of  atrophy  of  the  optic  nerve  and  in  central  scotoma. — One  of 
the  first  cases  of  this  kind  was  observed  at  the  clinic  of  Hansen 
Grut,  at  Copenhagen,  and  described  by  KrencheL  It  was  a 
patient  who  presented  himself,  saying  that  he  did  not  see  well 
enough  to  find  his  way.  Examined  with  the  ophthalmoscope, 
the  papillae  were  whitish,  the  visual  acuity  was  normal,  and  the 
visual  field  was  only  slightly  contracted.  It  was  puzzling,  there- 
fore, to  explain  the  complaints  of  the  patient  until  the  idea  of 
examining  him  with  the  disc  of  Masson  presented  itself:  the 
fraction  of  Fechner  had  increased  to  _L.  The  patient  distin- 
guished perfectly  black  on  white,  but  was  unable  to  distinguish 
between  gray  shades,  as  they  present  themselves,  for  example, 
in  street  paving ;  whence  the  difficulty  which  he  experienced  find- 
ing his  way. 

We  sometimes  meet  patients  who  claim  that  they  see  better 
when  the  illumination  is  low  (nyctalopia).  Examining  their 
visual  acuity,  we  find,  however,  that  it  does  not  increase  when 
we  lessen  the  illumination  (at  least  in  cases  in  which  we  have 
not  to  do  with  a  purely  optic  phenomenon :  this  is  why  a  central 
leucoma  becomes  less  annoying  when  the  pupil  is  dilated). — But, 


THE  LIGHT  SENSE  281 

on  comparing  these  persons  with  a  normal  person,  we  note  that 
by  lessening  the  illumination  the  acuity  of  the  normal  person 
diminishes  more  quickly  than  that  of  the  patient.  If  the  normal 
person  has  an  acuity  three  times  that  of  the  patient  by  ordinary 
illumination,  it  may  happen  that  on  diminishing  the  illumination 
both  would  have  the  same  visual  acuity.  Persons  suffering  from 
a  central  scotoma  sometimes  complain  of  nyctalopia  for  a  like 
reason.  We  have  seen,  indeed,  that  the  superiority  of  the  macula 
over  the  rest  of  the  retina  diminishes  with  the  illumination,  so 
that  with  a  very  weak  illumination  the  fovea  does  not  see  so 
well  as  the  rest  of  the  retina.  We  can  understand,  therefore, 
that  a  central  scotoma  may  cause  relatively  less  annoyance  when 
the  illumination  is  weak. 

We  must  recall,  too,  the  quantitative  measurement  of  the  light 
sense  in  persons  affected  with  cataract.  The  patient  ought  to  be 
able  to  recognize  the  illumination  of  an  ordinary  lamp  at  a  dis- 
tance of  4  to  5  meters,  or  that  of  a  candle  at  2  meters,  and  its 
projection  must  be  good,  that  is  to  say,  the  patient  must  be 
able  to  tell  the  direction  in  which  the  luminous  source  is  located. 
If  the  patient  does  not  satisfy  these  conditions,  we  may  conclude 
that  there  exists  an  affection  of  the  fundus  of  the  eye,  which 
compels  us  to  make  an  unfavorable  prognosis. 

Bibliography. — Bouguer  (P.)-  Essai  d'optique.  Paris,  1729. — Bouguer 
(P.).  Traite  d'optique  sur  la  gradation  de  la  lumiere.  Paris,  1760. — Lam- 
bert (J.  H.).  Photometria.  Augustas  Vindelie,  1760. — Masson.  Etudes  de 
photometric  electrique.  Ann.  de  physique  et  chimie,  1845,  t.  XIV,  p.  129. 
— Fcerster.  Veber  Hemeralopie  und  die  Anwendung  eines  Photometers  im 
Gebiete  der  Ophthalmologie.  Breslau,  1857. — Fechner.  Elemente  der  Psy- 
chophysiTc.  Leipzig,  1860,  2  vol. — Klein.  De  I'influence  de  Veclairage  sur 
I'acuite.  Paris,  1873. — Krenchel  (V.)  in  Klin.  Monatsbl.  fur  Augenheilk. 
February,  1880. — Bjerrum  (J.).  Undersoegelsen  of  Synet.  (Danish).  Co- 
penhagen, 1894.  Charpentier  (A.).  La  lumiere  et  les  couleurs.  Paris, 
Baillere,  1888. 

The  work  of  Lambert  is  first  in  importance.  A  German  translation  with 
notes  by  Anding  has  just  appeared  at  W.  Ostwald.  Die  Klassiker  der 
exakten  Wissenschaften.  Leipzig,  1892. 


CHAPTER  XVII 
THE  COLOR  SENSE 

103.  General  Remarks. — On  analyzing  any  color  with  the 
spectroscope,  we  find  no  other  tints  than  those  which  compose 
the  solar  spectrum,  mixed  in  different  proportions.  The  only 
colors  which  would  seem  to  form  an  exception,  the  brownish 
colors,  are  really  red  and  yellow  colors  of  slight  intensity,  more 
or  less  mixed  with  white.  To  examine  the  color  sense,  therefore, 
we  may  limit  ourselves  to  the  study  of  spectral  colors  and  their 
mixtures.  We  have  thus  the  advantage  of  experimenting  with 
pure  colors,  which  are  easily  definable  by  the  wave  length  of 
the  rays.  The  use  of  colored  papers,  although  very  convenient, 
has  many  drawbacks,  in  consequence  of  the  impossibility  of  de- 
fining exactly  the  color  of  the  paper  used,  so  that  another  ex- 
perimenter may  be  able  to  procure  a  similar  tint.  On  the  con- 
trary, if  we  obtain  a  result  with  spectral  light  of  a  certain  wave 
length,  the  experiment  may  be  described  in  a  very  exact  man- 
ner, the  only  condition  which  may  be  left  uncertain  being  the 
intensity  of  the  light  used.  On  analyzing  blue  spectral  light 
with  the  spectroscope  we  find  only  blue,  while  the  light  reflected 
by  a  paper  of  this  color  contains,  besides  blue,  most  of  the  other 
colors  of  the  spectrum.  There  is  another  way  of  procuring  pure 
colors,  for  the  incandescent  vapors  give  monochromatic  light,  at 
least  approximately.  Thus  the  sodium  flame  gives  yellow  light 
of  a  wave  length  of  0.59^,  the  lithium  flames  red  light  (0.67^), 
the  thallium  flame  green  light  (0.54^),  and  the  strontium  flame 
blue  light  (0.46^).  But,  as  a  rule,  these  flames  are  in  less  com- 
mon use  than  spectral  light.  The  light  which  passes  through 
colored  glasses  is  generally  far  from  being  monochromatic;  we 
must,  however,  except  red  glasses,  colored  with  oxide  of  copper, 
which,  when  they  are  a  little  dark,  allow  scarcely  any  but  red 
rays  to  pass.  Among  liquids  we  sometimes  use  the  solution  of 

282 


THE  COLOR  SENSE  283 

£ 

bichromate  of  potash,  which  absorbs  the  blue  extremity  of  the 
spectrum,  and  the  solution  of  sulphate  of  copper-ammoniac, 
which  absorbs  the  red,  the  yellow  and  part  of  the  green.  A 
mixture  of  both  allows  a  quite  pure  green  light  to  pass. 


I 

J   < 

* 

i 

>             i 

.                      I 

r                                                 i 

,                                                   1 

-> 

1, 

1  1 

60 

LLJJJ 

1    !    I   I    1    1 

SOI 

I    1     1       1 

I        1        |         1          1 

,       ,     1 

^  — 

J^i- 

—  ' 

A.  —     —  x^. 

—  S^. 

..  /^           .^- 

-A  

_x 

Red         Orange         Yellow         Green 


Blue 
II 


Indigo 


Violet 


H 


Red  Orange  Yellow  Green          Blue        Indigo       Violet 

Fig.  151. — I.    Spectrum  of  refraction. — II.    Spectrum  of  diffraction. 
The  numbers  indicate  the  wave  length  in  hundredths  of  p. 

We  distinguish  between  the  spectra  of  refraction,  formed  by 
means  of  prisms,  and  the  spectra  of  diffraction,  which  are  ob- 
tained by  allowing  light  to  pass  through  a  grating,  that  is  to  say, 
a  glass  plate  on  which  a  great  number  of  very  fine  parallel  lines 
have  been  traced. 

The  spectra  of  refraction  are  preferable  because  they  are, 
generally,  purer  than  the  spectra  of  diffraction.  They  have  this 
inconvenience  that  the  relative  width  of  the  different  colors 
varies  \vith  the  prism  used.  The  red  and  orange  colors  are  re- 
duced to  o.  relatively  small  space,  while  the  blue  and  violet  colors 
are  stretched  out  over  a  large  surface.  In  the  spectrum  of  dif- 
fraction, the  distance  between  the  different  colors  is,  on  the 
contrary,  proportional  to  the  difference  of  the  wave  length 
(fig.  151),  so  that  all  the  speclra  of  diffraction  are  alike  and 


284  PHYSIOLOGIC  OPTICS 

form,  so  to  speak,  the  normal  spectrum.  The  yellow  is  at  the 
middle  of  the  spectrum;  the  red  and  orange  occupy  half,  the 
green,  blue,  indigo  and  violet  the  other  half. 

As  landmarks  in  the  spectrum,  we  frequently  use  the  lines  of 
Fraunhofer,  the  wave  lengths  of  which  have  been  very  exactly 
determined.  Say,  for  example,  that  the  rays,  which  we  use, 
are  situated  at  half  the  distance  between  E  and  F;  on  the  scale 
of  figure  151  we  see  that  the  light  used  must  have  had  a  wave 
length  of  0.50  to  0.51^. — It  is  better,  however,  to  determine  the 
wave  length  directly,  which  is  easily  done  by  means  of  a  grating. 

I  have  already  observed  that  there  are  in  the  spectrum  rays 
beyond  the  red  which  are  not  visible.  The  extreme  visible  red 
corresponds  nearly  to  a  wave  length  of  0.8^.  The  colors  then 
follow  in  the  well-known  order :  red,  orange,  yellow,  green,  blue, 
indigo,  violet.  Beyond  the  violet  come  ultra-violet  rays,  which 
are  not  visible  under  ordinary  conditions,  but  which  can  be  ob- 
served by  means  of  a  photographic  plate,  or  by  receiving  them 
on  a  fluorescent  screen,  or  simply  by  eliminating  all  other  light 
according  to  the  method  given  on  page  131.  They  are  then  seen 
with  a  certain  grayish  color,  which  is,  perhaps,  partly  due  to 
the  fact  that  the  retina  is  fluorescent. 

We  distinguish  colors  according  to  their  hue  (tone),  their 
purity  or  tint  (saturation)  and  their  brightness  or  shade  (in- 
tensite).  The  tone  or  hue  depends  on  the  wave  length  alone, 
or,  in  other  words,  on  the  position  of  the  color  in  the  spectrum: 
the  red  has  a  different  hue  from  the  green,  etc.  The  saturation 
or  purity  depends  on  the  white  which  is  found  added  to  nearly 
all  existing  colors,  except  those  of  the  spectrum:  the  less  white 
there  is,  the  greater  the  purity  of  the  color.  The  intensity  or 
brightness  depends  on  the  quantity  of  light.  If  we  have  formed 
a  spectrum  by  means  of  a  certain  luminous  source,  and  then  in- 
crease the  intensity  of  this  source,  the  intensity  of  all  the  colors 
of  the  spectrum  increases  at  the  same  time. 

The  hue  changes  constantly  in  the  spectrum:  that  is  to  say, 
if  we  take  light  from  two  different  parts  of  the  spectrum,  we 
cannot  make  them  alike  by  changing  their  brightness.  The 
change  reaches  its  greatest  rapidity  in  the  green-blue  part  of 


THE  COLOB  SENSE 


285 


the  spectrum,  where  even  a  variation  in  the  wave  length  of 
o.ooiji  produces  a  change  of  hue;  the  rapidity  diminishes  towards 
the  extremity,  and  in  the  extreme  parts  of  the  red  and  violet 
the  hue  remains  the  same  (Kcenig  and  Dieterici). — According  to 
Kcenig  we  can  distinguish  about  160  different  hues  in  the  spec- 
trum. On  the  other  hand,  according  to  the  same  author,  the 
eye  can  distinguish  about  600  different  degrees  of  brightness  be- 
tween the  threshold  and  dazzling  light.  This  is  true  for  white 
and  probably  also  for  the  different  hues  of  the  spectrum,  but 
the  total  number  of  different  impressions  between  which  the  eye 
can  make  a  distinction  is,  however,  less  than  one  would  think 
in  view  of  these  indications,  for  when  the  brightness  becomes 
very  great  or  very  feeble,  the  color  disappears  as  we  shall  see 
forthwith. 


Green 


Yellowish-Green 


Bluish-Green 


Yellow 


Blue 


Indigo 


Violet 


Purple 

Pig.  152. — Table  of  colors  after  Newton. 

On  examining  the  spectrum  it  is  easy  to  see  that  our  sensations 
or  colors  form  a  continuous  series.  We  begin  with  the  red, 
which  passes  from  orange  to  yellow,  etc.,  and  end  with  the 
violet,  the  tint  of  which  presents  an  analogy  to  the  red.  The 


286  PHYSIOLOGIC  OPTICS 

intermediary  color  between  the  red  and  violet,  purple,  is  not 
found  in  the  spectrum,  but  it  would  be  possible  that  this  color 
would  be  produced  by  ultra-violet  rays  if  the  retina  were  not 
fluorescent. 

We  can,  therefore,  represent  the  gamut  of  the  colors  by  a 
closed  curve.  The  simplest  form  we  can  give  to  this  curve  is 
that  of  a  circle  (fig.  152),  replacing,  however,  the  part  corre- 
sponding to  the  purple  by  a  straight  line ;  we  shall  soon  see  why. 
We  suppose  all  the  colors  of  the  spectrum  placed  on  this  circle 
in  their  natural  order.  At  the  center  is  the  white,  and  on  the 
right,  going  from  the  white  to  one  of  the  spectral  colors,  are 
the  different  tints,  the  purity  being  greater  as  we  approach  the 
spectral  color.  If  we  mix  two  colors,  the  mixture  will  have  one 
of  the  intermediary  hues  often  bleached  with  white,  and  if  we 
mix,  in  suitable  proportions,  two  colors  situated  opposite  to  each 
other  on  the  table,  we  obtain  pure  white.  Two  colors  which, 
when  mixed,  give  white,  are  called  complementary.  For  this 
reason  red  is  complementary  to  green-blue,  green  to  purple, 
yellow  to  indigo  and  orange  to  blue. 

It  was  Newton  who  first  arranged  the  colors  as  in  this  table. 
We  find  in  it  all  hues  and  all  degrees  of  purity. 

I  must  add  a  few  words  on  the  sensation  of  black.  First,  it 
must  be  noted  that  black  produces  a  real  sensation:  to  see  black 
is  not  the  same  thing  as  to  see  nothing  at  all.  The  most  striking 
example  is  that  of  the  spot  of  Mariotte,  which  corresponds  to 
the  papilla.  In  this  spot  we  see  nothing,  but  we  do  not  see  it 
black.  By  looking  directly  in  front,  one  sees  a  part  of  the  space 
in  which  one  is;  in  regard  to  that  which  is  beyond  the  limits  of 
the  visual  field,  one  does  not  see  it,  but  it  does  not  appear  black. 
The  impression  of  black  is,  therefore,  a  true  sensation,  which 
corresponds  to  the  state  of  repose  of  the  visual  organ. 

There  exists  no  completely  black  object  in  nature:  even  black 
velvets  still  reflect  a  comparatively  considerable  quantity  of  light. 
A  black  object  placed  in  the  direct  light  of  the  sun  may  appear 
clearer  than  a  white  object  placed  in  the  shadow. 


THE  COLOR  SENSE  287 

According  to  some  measurements  which  I  have  made,  the 
whitest  paper  which  I  could  find  (visiting  cards)  returns  only 
about  a  third  of  the  incident  light  (37  per  cent.).  The  normal 
white  of  Kcenig,  which  is  obtained  by  burning  a  thread  of  mag- 
nesium and  allowing  the  vapor  to  be  deposited  on  a  sheet  of 
paper,  sends  back  about  two-thirds  of  the  light;  its  whiteness  is 
nearly  that  of  snow.  Ordinary  black  paper  (bristol  black)  re- 
turns nearly  5  per  cent,  of  the  incident  light  (1.5  per  cent,  of 
the  quantity  reflected  by  the  white  paper)  ;  black  velvety  paper 
sends  back  about  5  to  1000  of  the  incident  light  (1.5  per  1000 
the  quantity  reflected  by  white  paper).  The  most  absolute  black 
that  we  can  produce  is  that  of  an  aperture  made  in  the  side  of  a 
closed  box,  blackened  internally.  Compared  with  this  black  even 
the  velvety  paper  appears  slightly  grayish. 

Black  does  not  figure  on  the  table  of  Newton.  If  we  desire 
to  include  it  in  the  illustration,  we  must  suppose  the  colors  placed 
on  a  body  of  three  dimensions,,  a  pyramid  or  a  cone  (Lambert). 
The  .table  of  Newton  would  form  the  base  of  the  cone,  while 
the  black  would  form  its  apex :  on  the  conical  surface  we  would 
place  the  colors  of  little  intensity.  Thus  the  brown  would  be 
placed  between  the  yellow  and  the  black,  etc. 


104.  Phenomena  of  Contrast  (Simultaneous). — 'Our  judgment 
of  colors  is  always  influenced  by  the  colors  of  surrounding  ob- 
jects. This  fact  is  well  known  to  painters,  whose  color  sense 
is  generally  highly  developed,  so  that  they  often  see  colors  that 
inexperienced  persons  would  not  perceive.  But,  in  special  cir- 
cumstances, this  influence  makes  itself  felt  in  a  very  striking 
manner. 

i°  EXPERIMENT  OF  H.  MEYER. — Placing  a  small  piece  of  gray 
paper  on  a  sheet  of  colored  paper  and  covering  the  whole  with 
a  sheet  of  tissue  paper,  the  small  piece  is  seen  to  be  of  the  com- 
plementary color.  Pfluger  had  letters,  thus  arranged,  printed  for 
the  examination  of  color-blindness. 


288 


PHYSIOLOGIC  OPTICS 


2°  EXPERIMENT  OF  RAGONA   SCINA. — Two   sheets  of  white 
cardboard  (BC  and  BD,  fig.  153)  are  placed  so  as  to  form  be- 
,     ^  tween  them   a   right  angle;  on 

each  is  a  black  spot,  a,  b,  and  a 
red  glass  BE  is  placed  so  as  to 
form  an  angle  of  45  degrees 
with  the  cardboard.  The  eye  A 
receives  from  BC  the  rays  which 
have  passed  through  the  red 
glass  and  from  BD  the  rays  re- 
flected by  this  glass.  The  for- 
mer are  red,  the  latter  white,  so 
that  the  background  BC  would 
appear  whitish-red.  The  spot  a 
is  seen  at  a'  of  a  deep  red  color, 
because  the  eye  receives  at  this 
place  only  red  rays,  the  white 
rays  which  should  come  from 
BD  being  wanting.  Correspond- 
ing to  b  the  eye  receives  only 
white  rays  coming  from  BD,  and 
nevertheless,  b  appears  of  an 
intense  green  by  contrast.  The  experiment,  which  is  very  pretty, 
may  be  performed  with  other  colored  glasses.  We  always  see 
a'  and  b  in  complementary  colors. 


a/6  C 

Fig.  153. 
Experiment  of  Eagona  Scina. 


3°  COLORED  SHADOWS. — Let  A  and  B  (fig.  154)  be  two  can- 
dles, of  which  A  may  be  the  brighter;  in  front  of  A  we  place 
a  red  glass ;  a  and  b  are  the  shadows  which  the  stick  c  forms  on 
a  white  screen.  The  screen  illuminated  by  the  white  light  from 
B  and  the  red  light  from  A,  should  appear  whitish-red,  but  the 
red  is  scarcely  perceptible;  b,  which  is  illuminated  only  by  the 
red  light  from  A,  appears  red,  and  a,  which  should  appear  white, 
appears  green,  by  contrast.  We  can  also  make  the  experiment 


* 


THE  COLOR  SENSE  289 

with  daylight  and  that  of  a  candle,  in  which  case  there  is  no 
need  of  the  colored  glass,  since  the  colors  ^          6 

of  the  two  lights  already  differ.    We  be-  ~~X       7~~ 

gin  by  illuminating  the  screen  with  day-  \  / 

light;  we  see  the  screen  white  and  the  r\ 

shadow  black   (gray).     On  lighting  the  /     \ 

*  ' 

candle  the  screen  still  appears  white,  al-  / 

though  it  would  seem  that  it  ought  to 

appear  yellow,  since  it  is  partly  illumi- 

nated  by  the  yellow  light  of  the  candle; 

the   shadow,  which  just  now  appeared  Fig.  154. 

gray,  has  become  yellow  by  the  illumina- 

tion  of  the  candle,  and  the  other  shadow, 

which  receives  the  daylight,  appears  blue  "by  contrast." 

4°  EXPERIMENT  OF  DOVE.  —  Analogous  phenomena  with  colored 
.shadows  are  observed  when  we  place  a  colored  glass  opposite 
a  mirror.  We  then  see  two  images  of  a  white  object,  one  by 
reflection  on  the  anterior  surface  of  the  glass,  the  other  by 
reflection  on  the  mirror;  this  latter  has  the  color  of  the  glass, 
since  the  rays  have  passed  through  the  glass  twice.  The  first, 
which  ought  to  be  white,  shows  by  contrast  the  complementary 
color.  With  a  black  object  on  a  white  ground,  the  sash  of  a 
window  for  example,  we  have  the  phenomena  reversed. 

We  observe  that  the  expression  "by  contrast"  scarcely  explains 
these  singular  phenomena.  In  most  of  these  cases  it  seems 
that  the  fundamental  phenomenon  lies  in  the  defectiveness  of 
our  judgment  of  white.  Thomas  Young  already  directed  atten- 
tion to  the  fact  that  a  sheet  of  white  paper  appears  white  to 
us,  as  well  when  illuminated  by  the  yellow  light  of  a  candle  as 
by  the  red  light  of  a  coal  fire.  We  may  say  that  we  consider 
always  as  white  the  bodies  which  return  the  greatest  quantity 
of  light,  whatever  may  be  the  light  used  (Javal).  This  is  pri- 
marily independent  of  the  illumination,  and  this  is  why  a  sheet 
of  white  paper  appears  to  us  white  with  different  illuminations. 
But  the  recollection  of  the  illumination  by  daylight  plays,  never- 
theless, a  part,  so  that,  if  the  real  color  differs  much  from  it, 
the  paper  seems  white  with  a  slight  colored  tone:  thus  when 


290 


PHYSIOLOGIC  OPTICS 


we  look  at  it  through  a  red  glass,  in  which  case  the  paper  re- 
turns red  rays  only,  it  appears  a  reddish-white. 

In  the  experiment  with  colored  shadows  the  screen  appears 
to  us  white  when  it  is  illuminated  by  daylight  only,  and  also 
when  it  is  illuminated  by  a  mixture  of  daylight  and  candle  light 
at  the  same  time.  But  if,  under  these  circumstances,  the  whitish- 
yellow  light  which  illuminates  the  screen  appears  white  to  us, 
it  is  not  strange  that  the  white  light  which  illuminates  one  of 
the  shadows  appears  blue,  that  is  to  say,  less  yellow  than  the 
screen.  We  may  regard,  so  to  speak,  the  zero  of  the  scale  of 
our  color  sensations  (the  white)  displaced,  and  with  it  the  entire 
scale. 

TRUE   SIMULTANEOUS   CONTRAST. — While  the   phenomena   of 
which  we  have  just  spoken  are  due  to  a  false  judgment  of  the 


Fig.  155. — Disc  of  Masson. 

color  white,  there  are  others  which  are  due  to  a  true  contrast. 
By  making  a  disc  like  that  of  figure  155,  but  having  a  greater 
number  of  sectors,  rotate  we  obtain  gray  rings,  and  we  observe 
that  we  cannot  see  the  outer  rings  which  are  very  pale ;  we 
see  only  the  borders  of  each  ring:  the  external  border,  which 
appears  deeper  than  the  rest  of  the  ring,  by  contrast  with  the 
following  ring  which  is  paler,  and  the  internal  border  which 


THE  COLOR  SENSE  291 

appears  paler  than  the  rest,  by  contrast  with  the  neighboring 
darker  ring.  By  replacing  the  white  and  black  by  yellow  and 
blue,  we  obtain  rings  which  present  different  shades  of  gray; 
the  internal  rings  are  bluish,  the  external  rings  yellowish.  But 
each  ring  has  an  internal  border  which  is  yellow,  by  contrast 
with  the  preceding  ring  which  is  bluer,  and  an  external  border 
which  is  blue,  by  contrast  with  the  following  ring  which  is 
yellower.  The  phenomenon  is  very  pronounced,  but  disappears, 
at  least  in  a  great  part,  if  we  separate  the  rings  by  very  fine 
black  circles.  The  diffuse  borders  favor  considerably  the  effect 
of  the  contrast. 

105.  After-images  (Successive  Contrast). — When  we  look  at 
a  small  colored  surface,  placed  on  a  white  ground,  by  fixing 
exactly  the  same  point  for  a  short  time,  we  observe  that  the 
color  diminishes  gradually  in  brightness:  the  red  becomes 
brown,  etc.  We  observe  at  the  same  time  that  the  object  is 
surrounded  by  a  narrow  border  of  the  complementary  color, 
due  to  the  fact  that,  in  spite  of  himself,  the  observer  makes 
slight  changes  in  the  direction  of  the  look.  We  explain  the 
phenomenon  by  saying  that  the  part  of  the  retina  where  the 
image  is  formed  is  fatigued  for  the  color  in  question.  If  we 
then  transfer  the  look  to  a  sheet  of  white  paper,  we  see  an 
image  tinted  with  the  complementary  color.  If  the  surface  be 
red,  the  image  appears  bluish-green.  We  may  suppose  the  white 
color  as  composed  of  two  complementary  colors,  red  and  green; 
the  retina  being  fatigued  for  the  red  color,  it  is  the  green  color 
which  predominates.  If  the  object  we  look  at  is  white,  the 
after-image  is  black;  but  if  we  look  at  a  flame  or  other  very 
bright  object,  we  obtain  a  colored  after-image,  the  color  of 
which  changes  before  its  disappearance. 

The  after-images  of  the  complementary  color  are  called  nega- 
tive: we  can  also  obtain  positive  images,  each  part  of  which  has 
the  same  color  as  the  original.  We  close  the  eyes  and  cover 
them  with  the  hand  for  some  minutes,  so  that  no  light  can  enter 
the  eye.  We  keep  in  this  position  for  some  time  until  all  prior 
impressions  on  the  retina  have  disappeared.  This  done,  we  re- 
move the  hand  and  open  the  eyes  for  an  instant,  without,  how- 


292  PHYSIOLOGIC  OPTICS 

ever,  changing  the  direction  of  the  look,  shut  them  immediately 
and  cover  them  again.  If  the  experiment  is  very  successful, 
we  then  see  a  positive  image  of  exterior  objects,  of  a  surprising 
distinctness.  We  can  scarcely  believe  that  we  have  really  closed 
cur  eyes;  the  hand  seems  transparent.  If  we  continue  to  keep 
the  eyes  closed,  we  see  the  less  illuminated  parts  of  the  image 
disappear,  while  the  more  illuminated  parts  change  color,  be- 
coming bluish,  violet,  orange,  etc.;  the  image  disappears  and 
returns  again,  and  so  forth. 

A  clear  after-image  of  a  chess-board,  or  other  analogous  figure, 
shows  phenomena  exactly  like  those  which  I  shall  describe  later 
under  the  heading  "Phenomenon  of  Troxler."  It  now  becomes 
probable  that  the  disappearance  and  reappearance  of  the  after- 
images are  due  to  the  same  causes,  likewise  unknown,  as  this 
phenomenon.  The  after-images,  of  which  I  have  just  spoken, 
last  for  a  relatively  long  time,  but  there  are  others  which  last 
so  short  a  time  that  they  escape  observation  in  the  ordinary 
distances  of  life.  The  simplest  way  of  making  them  appear 
consists  in  moving  the  object  which  is  intended  to  produce  them. 
The  secondary  image  then  seems  to  follow  the  object  because 
it  is  former  at  the  place  where  the  object  was  a  moment  before, 
and  because  it  lasts  only  an  instant.  Ordinary  after-images 
form,  in  these  circumstances,  a  long  luminous  series.  The  most 
striking  of  these  phenomena  was  described  by  Purkinje  and  later, 
under  the  name  of  "recurrent  vision,"  by  Davis.  The  experi- 
ment is  very  easy  to  perform:  we  light  a  match  in  darkness, 
blow  out  the  flame  and  move  the  burning  wood  around.  We 
shall  then  see  the  blue  after-image,  feebly  luminous  but  bright 
nevertheless,  follow  the  match  at  some  distance,  reproducing  its 
form  exactly.  There  are  two  conditions  necessary  to  the  suc- 
cess of  the  experiment :  one  is  that  we  do  not  follow  the  match 
with  the  look,  for  the  phenomenon  is  visible  only  in  indirect 
vision;  the  other  is  that  we  use  the  proper  speed,  neither  too 
fast  nor  too  slow.  Writh  a  certain  rate  of  speed  the  image 
(called  "ghost"  by  English  writers)  seems  double.  According 
to  Bidwell  the  interval  between  the  match  and  the  after-image 
corresponds  to  almost  one-fifth  of  a  second.  This  author  sees 


THE  COLOR  SENSE  293 

die  space  between  the  match  and  the  remainder  of  the  field 
blacker,  an  observation  which  was  confirmed  by  Agabobon,  who 
repeated  the  experiment  at  the  Sorbonne,  but  I  have  not  been 
able  to  verify  it. 

By  making  a  black  disc  with  a  white  sector  rotate  in  full 
sunlight  Charpentier  observed  a  black  sector  which  formed  in 
the  white  sector  not  far  from  its  anterior  border,  and  which 
was  sometimes  followed  by  several  others  less  pronounced.  At 
times  the  interval  between  the  anterior  border  of  the  white 
sector  and  that  of  the  black  sector  corresponded  to  about  J_  of 
a  second.  The  observation  indicates  that  when  we  allow  an 
illumination  to  act  for  a  very  short  period  on  the  retina  the 
latter  becomes  insensible  to  it  after  a  sixtieth  of  a  second  to 
reacquire  its  sensibility  after  the  lapse  of  the  same  period ;  some- 
times the  phenomenon  is  repeated  several  times  (retinal  oscilla- 
tions}. The  phenomenon  must  not  be  confounded  with  "recur- 
rent vision"  for  which  the  interval  is  much  longer. 

106,  Phenomena  Dependent  on  the  Variation  of  the  Brightness 
of  the  Colors. —  The  brightnesses  of  two  sources  of  light  of  the 
same  color  are  compared  as  easily  as  if  there  was  a  question 
of  white  light,  and  we  find  almost  the  same  value  for  the  frac- 
tion of  Fechner.  If  we  attempt  to  compare  lights  of  different 
color  the  eye  manifests,  on  the  contrary,  a  very  great  uncertainty, 
and  besides  we  encounter  a  difficulty  caused  by  what  is  called 
the  phenomenon  of  Purkinje.  Suppose  that  we  have  two  sources 
of  white  light,  which  we  have  found  of  equal  brightness.  If 
then  we  diminish  the  intensity  of  both  one-half  we  shall  find 
them  again  equal.  But  if  we  equalize  two  sources,  one  of  which 
is  blue  and  the  other  red,  and  that  then  we  diminish  their  bright- 
ness one-half,  the  blue  light  will  appear  much  brighter  than  the 
red  light. — Let  us  select  two  papers,  one  red  and  one  blue, 
which  by  daylight  illumination  appear  to  have  the  same  bright- 
ness; by  diminishing  the  illumination  the  blue  paper  will  ap- 
pear brighter  than  the  red  paper.  With  a  very  feeble  illumina- 
tion the  red  paper  will  appear  black,  the  blue  paper  a  pale 
gray.  In  order  that  the  experiment  may  succeed  well  the  papers 


294  PHYSIOLOGIC  OPTICS 

must  be  seen  under  an  angle  which  is  not  too  small,  for  the 
phenomenon  is  but  slightly  pronounced  for  the  macula.  In  ac- 
cordance with  these  observations  Mace  de  Lepinay  and  Nicati 
have  shown  that  the  visual  acuity  falls  much  more  quickly  on 
diminishing  the  illumination  when  we  use  red  light  than  when 
we  use  blue  light :  we  select  a  red  glass  and  a  blue  glass  so  that 
we  may  have,  by  daylight  illumination,  the  same  acuity  on  look- 
ing at  the  chart  through  either.  If  then  we  close  the  shutters 
almost  completely  so  as  to  greatly  diminish  the  illumination, 
we  observe  that  the  blue  glass  enables  us  to  still  read  half  of 
the  chart,  while  with  the  red  glass  we  cannot,  at  the  first  mo- 
ment, distinguish  even  the  chart;  after  a  little  while  we  can 
read  the  large  letters,  but  the  acuity  for  the  red  always  remains 
lower  than  the  acuity  for  the  blue  which  is  stationary.  Kcenig 
and  Brodhun  also  have  shown  that  the  increase  of  the  fraction 
of  Fechner,  at  the  lower  limit,  begins  sooner  for  the  red  than 
for  the  blue. 

The  following  experiment  shows  in  a  very  striking  manner 
the  difference  which  exists  in  this  regard  between  the  two  ex- 
tremities of  the  spectrum.  We  project  the  spectrum  on  a  screen 
A,  pierced  by  two  apertures,  allowing  the  red  rays  and  the 
blue  and  violet  rays  to  pass.  Behind  the  screen  A  we  place  a 
lens  which  reunites  these  rays  on  a  second  screen  B,  forming 
on  it  an  image  of  the  surface  of  the  prism  which  is  turned 
towards  A.  This  image  then  shows  a  pretty,  purple  color.  In 
front  of  the  screen  B  we  place  a  stick  which  forms  thereon 
two  shadows,  one  red,  the  other  blue,  and  it  is  easy  to  so  regu- 
late the  apertures  of  the  screen  A  that  both  shadows  may  have 
the  same  brightness.  If  we  now  diminish  the  width  of  the  slit 
through  which  light  reaches  the  prism  the  purple  is  diluted 
more  and  more  with  white.  The  blue  shadow  becomes  grayish, 
and  brighter  and  brighter  compared  with  the  background,  while 
the  red  shadow  retains  its  color,  but  becomes  darker  and  darker. 
Finally  it  is  nearly  black  and  alone  visible,  the  other  shadow 
being  gray  and  having  nearly  the  same  brightness  as  the  back- 
ground. 


THE  COLOR  SENSE  295 

In  the  spectrum  it  is  the  yellow  and  green  rays  which  have 
most  brightness.  The  brightness  diminishes  towards  the  two 
extremities  of  the  spectrum,  but  more  towards  the  blue  ex- 
tremity than  towards  the  red  extremity.  We  must  note,  how- 
ever, that  if  the  blue  and  violet  colors  seem  relatively  feeble  in 
the  prismatic  spectrum,  this  is  partly  due  to  the  fact  that  these 
colors  are  spread  over  a  much  greater  space  than  the  others. 
In  the  spectrum  of  diffraction  the  intensity  is  greatest  in  the 
middle  of  the  spectrum,  and  diminishes  almost  alike  towards 
the  two  extremities. 

If  we  lessen  the  intensity  of  the  luminous  source  the  colors 
of  the  spectrum  change  hue.  We  first  see  the  yellow  and  blue 
colors  disappear;  there  remain  only  the  red,  green  and  violet, 
which  take  the  place  of  the  colors  which  have  disappeared.  On 
still  further  diminishing  the  brightness,  the  blue  changes  into  a 
blue-gray,  the  green  into  a  green-gray,  the  red  becomes  brown- 
ish and  finally  all  the  colors  disappear,  and  we  see  only  gray. 
The  red  alone  forms  an  exception;  it  does  not  seem  to  change 
into  gray  before  disappearing. 

There  exists  a  very  pretty  method  of  showing  the  change  of 
appearance  of  the  spectrum  by  the  diminution  of  the  bright- 
ness. It  consists  in  gluing  a  board  of  velvety  black  paper  on  a 
white  screen  so  that  by  projecting  on  it  a  horizontal  spectrum 
the  upper  half  is  formed  on  the  black  paper  and  the  lower  half 
on  the  white  screen.  This  latter  half  shows  the  spectrum  as 
it  ordinarily  appears,  while  the  upper  half  has  the  form  of  a 
gray  band,  with  the  exception  of  the  part  corresponding  to  the 
red  which  appears  brown. 

The  colors  disappear,  therefore,  when  the  brightness  of  the 
rays  becomes  very  feeble.  Also  when  the  brightness  becomes 
very  strong  the  impression  approaches  white.  The  sun,  seen 
through  a  red  glass,  appears  a  whitish-yellow,  although  the  glass 
allows  only  red  rays  to  pass.  Concentrating  the  light  of  the  sun 
on  a  sheet  of  white  paper  with  a  lens,  after  having  made  it  pass 
through  a  blue  glass,  the  image  of  the  sun  appears  white.  When 
we  look  at  the  sun  through  a  prism  the  spectrum  presents  itself 
as  a  colorless  strip  of  a  dazzling  brightness.  Here  also  it  is  the 


296 


PHYSIOLOGIC  OPTICS 


red  which  best  maintains  its  color;  in  most  cases  it  appears  a 
whitish-yellow. 

According  to  Parinaud,  these  phenomena  depend  on  the  adap- 
tation of  the  eye.  The  spectrum  of  feeble  brightness,  which 
appears  gray  to  the  adapted  eye,  is  invisible  to  the  eye  not 

ABCD  EF  C  H 


0 

100 
200 
£00 


1000 


\ 


Fig.  156. — After  Parinaud. 

adapted,  and  when,  the  intensity  increasing,  it  becomes  visible 
to  the  non-adapted  eye  it  in  turn  appears  colored.  Parinaud 
determined  the  threshold  for  different  rays  of  the  spectrum,  and 
found  the  curves  represented  by  figure  156.  The  upper  curve 
is  that  of  the  adapted  eye,  the  lower  curve  that  of  the  eye  not 


TEE  COLOE  SENSE  297 

adapted.  The  different  parts  of  the  spectrum  are  indicated  by 
the  vertical  lines,  prolongations  of  the  lines  of  Fraimhofer  in 
the  diagram  of  the  spectrum  which  is  above  the  figure.  The 
numbers  on  the  left  indicate  the  quantities  of  light  necessary 
in  order  that  these  different  parts  of  the  spectrum  may  be  per- 
ceived. Thus  the  adapted  eye  requires  a  quantity  of  light  equal 
to  i  (this  quantity  being  taken  as  the  unit)  in  order  to  perceive 
the  green  rays  near  E,  while  the  non-adapted  eye  requires  a 
quantity  equal  to  100  in  order  to  perceive  the  same  rays,  and 
a  quantity  equal  to  1500  to  perceive  the  blue  rays  near  G.  We 
see  that  the  eye,  by  adaptation,  gains  nothing  for  the  percep- 
tion of  red  rays,  whilst  it  gains  enormously  for  the  more  re- 
frangible rays.  But  it  gains  only  in  luminous  sensibility :  except 
the  part  be,  which  is  common  to  the  two  curves,  the  whole  upper 
curve  corresponds  to  colorless  sensations  only.  According  to 
Parinaud,  the  fovea  gains  nothing  by  adaptation;  the  rays  also 
appear  colored  as  soon  as,  with  increasing  brightness,  they 
become  visible  to  the  fovea. 

The  results  of  Parinaud  have  been  disputed  by  Charpentier, 
and  they  no  longer  harmonize  well  with  the  experiments  men- 
tioned on  page  294.  According  to  Charpentier,  it  is  wrong  to 
attribute  the  colorless  sensation  which  the  rays  of  very  feeble 
brightness  call  forth  to  the  adaptation  of  the  eye,  and,  on  the 
other  hand,  it  is  certain  that  if,  from  full  daylight,  we  enter  a 
relatively  dark  space,  we  cannot  distinguish  right  away  colors 
which  we  observe  very  well  later. 

Nevertheless,  adaptation  plays  a  considerable  part  in  relation 
to  these  phenomena  as  the  following  observation  of  Charpentier 
shows.  He  covered  the  plate  B  of  his  photoptometer  (see  page 
275)  with  a  black  paper,  pierced  with  seven  small  openings 
grouped  in  a  space  of  nine  millimeters  square.  The  plate  A 
was  illuminated  by  spectral  light  of  different  colors.  Oil  open- 
ing gradually  the  diaphragm  of  the  instrument,  he  proved  that 
the  first  impression  which  is  obtained  is  that  of  a  diffuse  lu- 
minous spot,  without  color;  let  us  designate  the  aperture  of  the 
diaphragm  for  the  moment  by  a.  To  distinguish  the  color  it 
was  necessary  to  give  the  diaphragm  a  larger  aperture  b,  and 


298  PHYSIOLOGIC  OPTICS 

it  is  only  by  making  the  aperture  still  greater  c  that  we  come 
to  distinguish  the  points.  For  the  eye,  adapted  to  darkness,  the 
apertures  b  and  c  remain  almost  the  same  as  for  the  non-adapted 
eye,  while  the  aperture  a  diminishes  enormously  especially  for 
the  more  refrangible  colors. 

It  is  not  strange  that  there  exist  differences  of  opinion  on 
these  questions,  for  there  is  very  little  certainty  in  the  deter- 
mination of  the  lower  limits  of  the  sensations.  It  must  also  be 
noted  that  the  expressions  "adapted"  and  "non-adapted"  ap- 
plied to  the  eye  are  vague.  If  every  one  is  in  accord  in  con- 
sidering an  eye  adapted  when  it  remains  for  half  an  hour  in 
darkness,  or  non-adapted  when  it  remains  as  long  in  full  day- 
light, the  authors  do  not  agree  so  well  in  designating  the  state 
of  the  eye  when  exposed  to  an  intermediary  illumination,  such 
as  that  of  the  interior  of  our  houses. 

107.  Methods  of  Mixing  Colors. —  The  fundamental  examina- 
tion of  the  color  sense  is  made  by  means  of  what  is  called 
equations  of  colors:  we  mix  two  or  three  colors  in  different 
proportions  until  the  observer  declares  the  mixture  similar  to 
a  fourth  given  color,  most  frequently  white.  We  then  examine 
whether  an  eye,  of  which  the  color  sense  is  normal,  recognizes 
the  equation,  that  is  to  say,  whether  the  mixture  appears  likewise 
similar  to  white  for  this  eye. — We  can  mix  the  two  colors  in 
different  ways. 

i°  Mixtures  of  Spectral  Colors.  We  form  two  spectra  by 
means  of  two  prisms,  and  by  allowing  these  spectra  to  slide 
over  one  another  we  can  mix  any  two  hues  from  them.  Helm- 
holtz  accomplished  the  same  end  with  a  single  prism,  by  using 
a  slit  in  the  form  of  V ;  each  of  the  branches  formed  an  oblique 
spectrum,  and  the  two  spectra  would  overlap  to  a  great  extent 
so  that  we  could  obtain  all  possible  mixtures. 

The  apparatus  of  Maxwell  was  very  ingenious.  It  consisted 
of  a  box,  a  section  of  which  is  shown  in  figure  157.  At  E  is 
a  narrow  slit  through  which  passes  light,  which  is  reflected  by 
the  mirror  e  towards  the  prisms  P  and  P1?  through  which  it 
passes  to  meet  the  concave  mirror  S.  This  mirror  reflects  the 


THE  COLOR  SENSE  299 

light  which  passes  again  through  the  prisms  to  go  to  form  a 
spectrum  on  the  far  end  of  the  box,  AB.  At  this  place  are 
three  movable  slits  x,  y  and  z,  which  permit  spectral  light  of 
any  hue  to  leave  the  box  through  each  of  the  slits  by  displacing 
them. — Suppose  x  corresponds  with  the  red,  y  with  the  green 
and  s  with  the  violet.  It  must  be  noted,  in  consequence  of  the 
reversibility  of  optic  processes,  that  if  we  illuminate  the  slit  x 
from  the  outside  by  red  light,  this  light  will  reach  an  eye  placed 
at  E;  but  if  we  illuminate  the  same  slit  with  green  light,  this 


£ 

Fig.  157.— "Color  box"  of  Maxwell. 

light  will  not  reach  an  eye  at  E,  but  will  be  projected  to  one 
side  of  E.  In  order  that  the  green  light  reach  E,  it  must  pass 
through  the  slit  y.  Consequently  the  three  slits  x,  y  and  z  by  a 
white  luminous  source,  an  eye  placed  at  E  sees  the  surface  of 
the  prism  P  colored  by  the  mixture  of  the  three  colors,  which 
a  flame  placed  at  E  would  project  on  the  slits  x,  y  and  z. — At 
the  far  end  of  the  box  is  yet  another  aperture  c  through  which 
enters  white  light,  which,  after  having  been  reflected  by  the 
mirror  M  and  concentrated  by  the  lens  L,  meets  a  plate  of 
ground  glass  blackened  on  the  back  Mr  The  eye  placed  at  E 
sees  this  plate  at  the  side  of  the  prism,  and  can  thus  compare 
the  brightness  and  color  of  the  mixture  with  that  of  the  white 
light,  admitted  through  c.  By  properly  placing  and  opening  the 
slits,  we  can  thus  obtain  a  mixture  which  is  not  distinguishable 
from  the  white  light  reflected  by  Mlf  either  as  to  color  or  bright- 
ness. 

The  latest  researches  on  the  mixtures  of  colors  (Kcenig  and 
his  pupils)   have  been  made  with  a  large  spectral  instrument, 


300  PHYSIOLOGIC  OPTICS 

which  was  constructed  for  the  laboratory  of  Berlin,  and  a 
description  of  which  is  found  in  the  second  edition  of  Helm- 
holtz's  work  on  Physiologic  Optics  (page  355). 

2°  Maxwell  also  studied  the  mixtures  of  colors  by  placing, 
on  the  disc  of  Masson,  sectors  of  different  colors  (see  page  313). 

3°  We  can  mix  colors  by  means  of  a  plate  of  glass  ab  (fig. 
158),  which  is  held  so  that  it  may  reflect  rays  of  one  color  at 
the  same  time  that  it  allows  rays  of  another  color  to  pass  (Lam- 
bert). 


\ 


Yellow  Blue 

Pig.  158. — Mixture  of  colors  by  means  of  a  glass  plate. 

4°  Looking  at  two  colors  placed  side  by  side  through  a  double 
refracting  prism,  we  see  them  separated  by  a  strip  the  colora- 
tion of  which  is  that  of  the  mixture. 

5°  Placing  two  glasses  of  different  colors  before  the  two 
openings  in  the  experiment  of  Scheiner  and  looking  at  the  sky, 
we  see  the  common  part  of  the  circles  of  diffusion  in  the  color 
of  the  mixture. 

6°  Painters  frequently  use  mixtures  of  coloring  matter,  but 
the  results  which  are  thus  obtained  are  frequently  not  in  accord 
with  those  which  are  obtained  by  the  other  methods.  The  best 
known  example  is  the  mixture  of  yellow  and  blue.  Painters 
thus  obtain  green,  while  with  a  revolving  disc  we  obtain  a  gray- 


THE  COLOR  SENSE  301 

white  (Lambert).  Helmholtz  gave  the  following  explanation  of 
this  difference:  mixing  the  colors  of  yellow  and  blue  pigment 
the  superficial  molecules  send  back  yellow  light  and  blue  light. 
Together  these  rays  produce  the  impression  of  white,  as  on  the 
revolving  disc.  The  blue  molecules  situated  deeper  also  send 
back  blue  light,  but  it  must  be  noted  that  this  blue  light,  as  also 
that  of  the  superficial  molecules,  is  not  pure :  by  the  spectroscope 
we  find  that  it  contains  green,  blue  and  violet  rays.  The  yellow 
molecules  send  back  red,  yellow  and  green  rays.  Generally  the 
molecules  allow  to  pass  rays  of  the  same  color  as  those  which 
they  send  back.  Among  the  rays  reflected  by  the  deep  yellow 
molecules,  only  green  rays,  therefore,  can  pass  through  the 
superficial  blue  molecules,  and,  among  those  reflected  by  the 
deep  blue  molecules,  likewise  only  the  green  rays  can  pass 
through  the  superficial  yellow  molecules.  The  result,  therefore, 
becomes  a  green  color,  mixed  with  the  white  reflected  by  thp 
surface. 

108.  Results  of  the  Mixtures  of  Colors. —  Newton  devised  his 
table  to  give  a  graphic  illustration  of  the  results  which  are  ob- 
tained by  mixing  colors.  The  principle  of  this  table  is  that  all 
the  colors  we  can  produce  by  mixing  two  given  colors  are  placed 
on  the  straight  line  which  joins  these  two  colors,  and  so  much 
nearer  to  that  one  of  the  two  colors  which  enters  most  into 
the  mixture.  The  quantity  of  the  color  of  the  mixture  is  ex- 
pressed by  the  sum  of  the  quantities  of  the  component  colors. 
Suppose,  for  example,  that  we  want  the  result  of  the  mixture 
of  three  parts  of  green  with  one  part  of  red  and  two  parts  of 
blue.  We  begin  by  joining  the  green  and  red  by  a  straight 
line  which  is  divided  into  two  by  the  point  p  (fig.  159),  so  that 
the  distance  of  p  from  the  green  may  be  a  third  of  its  distance 
from  the  red;  p  is  then  the  place  of  the  mixture  of  the  green 
and  red,  the  mixture  being  represented  by  the  number  4,  the 
sum  of  the  two  component  colors.  We  then  join  the  point  p 
with  the  blue  by  a  second  straight  line  which  is  divided  into 
two  by  the  point  q,  so  that  the  distance  pq  is  to  the  distance  of 


302  PHYSIOLOGIC  OPTICS 

q  from  the  blue,  in  the  proportion  of  2  to  4;  q  is  the  place  of 
the  mixture  of  the  three  colors,  and  the  quantity  of  this  mix- 
ture is  expressed  by  the  number  6.  Drawing  the  line  oq  and 
prolongating  it  until  it  cuts  the  spectral  curve,  we  see  that  the 
color  of  the  mixture  is  a  bluish-green  strongly  diluted  with 
white. 

There  enters  into  this  illustration  of  Newton  an  expression 
which  is  not  defined,  that  of  the  quantity  of  the  colors.  While 
it  is  easy  to  tell  what  must  be  expected  from  equal  quantities 
of  the  same  color,  it  is  not  easy  to  define  the  expression  of  equal 
quantities  of  two  different  colors,  the  result  of  which  is  that 
the  form  of  the  curve  becomes,  up  to  a  certain  point,  arbitrary. 
With  Newton,  we  must  consider  as  equal  the  quantities  of  two 
complementary  colors,  which,  when  mixed,  give  white,  since 
the  white,  on  his  table,  is  situated  at  an  equal  distance  from 
both.  If  we  take  two  other  complementary  colors,  we  must 
also  consider  as  equal  the  quantities  of  these  colors  which,  mixed, 
give  white,  but  on  condition  that  this  white  be  of  the  same 
brightness  as  the  former.  As  we  shall  see,  Maxwell  and  Helm- 
holts  used  other  definitions. 

The  table  of  Newton  shows  that,  with  the  exception  of  purple, 
we  cannot  produce  new  colors  by  mixing  spectral  colors,  for  we 
can  always,  after  having  found  the  position  of  the  mixture, 
draw  a  straight  line  passing  through  the  center  and  this  point. 
Prolonged,  this  straight  line  will  meet  a  spectral  color,  and  the 
mixture  is  equal  to  this  color  diluted  with  white. 

The  table  of  Newton  indicates  also  another  peculiarity  of  the 
normal  color  sense,  namely  the  fact  that  we  can  reproduce  all 
existing  hues  by  mixing,  two  by  two,  three  colors  properly  chosen. 
Let  us  select,  for  example,  red,  green  and  blue,  and  draw  on 
the  table  (fig.  159)  straight  lines  which  join  these  colors.  If, 
then,  we  select  any  spectral  color,  we  can  always  join  it  to  the 
center  of  the  table  by  a  straight  line;  this  straight  line  must 
necessarily  cut  one  of  the  sides  of  the  red-green-blue  triangle 
and  at  the  place  of  intersection  is  found  the  mixture  which  is 
similar,  in  hue,  to  the  spectral  color.  On  account  of  this  pe- 
culiarity the  normal  eye  is  called  trichromatic.  Observe  partial- 


TEE  COLOR  SENSE 


303 


larly  that  I  have  said  that  the  two  colors  are  alike  as  to  hue. 
Generally  they  are  not  alike  as  to  purity,  the  color  of  the 
mixture  being  diluted  with  white.  The  table  of  Newton  also 
requires  that  the  spectral  color  must  always  have  greater  purity, 
for,  if  we  could,  by  mixing  two  spectral  colors,  reproduce  a 
third  color  exactly,  these  three  colors  should  be  placed  on  a 
straight  line,  and  the  spectral  curve  could  not  be  circular.  But 
this  last  condition  of  the  table  is  not  fulfilled. 


Green 


Yellowish-Green 


Bluish-Gieen 


Yellow 


Blue 


Oi>anj>e 


Violet 


Purple 

Fig.  159.— Table  of  colors  after  Newton. 

The  accuracy  of  the  illustration  of  Newton  has,  indeed,  been 
verified  by  the  admirable  works  of  Maxwell.  This  author  found 
that  Newton's  table  gives  a  very  exact  illustration  of  the  results 
of  the  mixtures  of  colors,  but  that  the  spectral  colors  cannot 
be  arranged  in  a  circle,  because  there  are  quite  extended  parts 
on  the  spectrum,  the  colors  of  which  can  be  reproduced  exactly, 
or  nearly  exactly,  by  the  mixture  of  two  given  colors,  and  which, 
consequently,  must  be  placed  on  straight  lines. 

Figure  160  shows  the  spectral  curve  of  Maxwell.  While  the 
curve  of  Newton  must  be  considered  merely  as  a  conception  of 


304 


PHYSIOLOGIC  OPTICS 


the  mind,  Maxwell  determined  his  experimentally  with  the  in- 
strument described  in  the  preceding  chapter  (fig.  161).  To  use 
it  he  placed  it  in  such  a  position  that  the  slits  x,  y  z  and  c  were 
turned  towards  a  sheet  of  white  paper  illuminated  by  the  sun. 
As  a  starting  point  he  selected  the  three  following  colors 

(standard  colors)  : 

Bed  (E)  Green  (O)  Blue  (Bl) 


Wave  length:  0.630^ 


0.528 


0.457 


S» 


bellow 


62, 


.50       Bluish -G'recu 


Red 


/       Purple  „ 

Fig.  160. — Color  table  of  Maxwell. 


B1H 
Violet 


He  placed  the  slits  x,  y  and  z  so  as  to  give  access  to  these 
colors,  and,  by  regulating  the  width  of  the  slits,  he  produced  a 
mixture  which  differed  neither  in  tint  nor  brightness  from  white 
introduced  through  the  slit  c. 


THE  COLOR  SENSE  305 

By  measuring  the  slits  he  found  for  x  a  width  of  2.36  mm., 
for  y  3.99  mm.  and  for  z  3.87  mm.,  and  by  designating  the  white, 


E 

Fig.  161.— " Color  box"  of  Maxwell. 

which  remained  constant  through  all  the  experiments,  by  W, 
he  had  thus  the  equation 

2.36  E  -f  3.99  G  +  3.87  Bl  —  W 

He  then  displaced  the  slit  x  so  as  to  give  access  to  orange 
light ;  by  regulating  the  slits  he  again  produced  a  mixture  similar 
to  white  which  gave  him  the  equation. 

2.04  Or  +  3.25  G  -f-  3.88  Bl  =  W 

As  white  was  the  same  in  both  cases,  we  can  combine  the  two 
equations,  which  gives 

2.04  Or    -f  3.25  G  -f  3.88  Bl  =  2.36  E  -f  3.99  G  -f-  3.87  Bl 
or 

2.04  Or  =  2.36  E  -f  0.74  G  —  0.01  Bl 
or 

1  Or  =  1.155  B  -f-  0.362  G  —  0.006  Bl 

He  then  repeated  the  measurement  for  the  other  colors,  by 
always  combining  two  of  the  standard  colors  with  the  color  in 
question  to  produce  white.  He  thus  succeeded  in  expressing 
all  the  colors  of  the  spectrum  by  three  colors.  The  following 
table  shows  the  results  of  these  measurements  (see  next  page). 

By  dividing  each  equation  by  the  coefficient  on  the  left,  we 
obtain  the  expression  corresponding  to  the  width  of  the  slit  of 
I  millimeter. 


306 


PHYSIOLOGIC  OPTICS 


Under  this  form  the  result  is  found  expressed  on  figure  162. 
The  three  curves,  designated  by  R,  G,  B,  correspond  to  the  three 
standard  colors;  the  numbers  underneath  are  the  wave  lengths 


COLOB 

I 

Rq    w 

i 

§ 

i 

t 

9 

ID 

*  § 

(4 

0 

9 

cc 

E 
p 

0- 

3 

Bed 

^     5.63 

(663)  = 

=           2.36   -f 

-  0.05  -| 

-  0.36 

2.77 

2.032 

1    2.36 

(630)  = 

=         2.36  4 

o.oo  4 

-  0.00 

2.36 

1 

Orange  

2.04 

(606)   = 

:           2.36   -f 

0.74  - 

-  0.01 

3.09 

0.662 

f    2.79 

(583)   = 

2.36  4 

2.45  - 

-  0.01 

4.80 

0.582 

Yellow  

3.20 

(562)   - 

=         1.55  4 

3.99  - 

-  0.10 

5.43 

0.589 

1  3.30 

(544)    = 

-         0.42  4 

-  3.99  - 

-  0.03 

4.38 

0.754   | 

(    3.99 

(528)   = 

r           0.00   4 

3.99  4 

-  0.00 

3.99 

1 

Green  

5.26 

(513)   = 

=  —  0.33  4 

3.99  4 

-  0.44 

4.10 

1.282 

<-    7.87 

(500)   = 

=  —  0.43  4 

3.99  4 

-  2.22 

5.77 

1.363 

f    7.83 

(488)   = 

:   —   0.39   4 

2.67  4 

-  3.87 

6.15 

1.275 

Blue  

1    5.14 

[    4.28 

(477)   = 
(467)   = 

:   —   0.24   4 
:   —   0.14   -f 

0.98  4 
0.14  4 

-  3.87 
-  3.87 

4.61 
3.87 

1.116 
1.105 

3.87 

(457)   = 

:            0.00    4 

0.00  4 

-  3.87 

3.87 

1 

Indigo  H 

4.10 

(449)   = 

0.08  4 

0.03  4 

3.87 

3.98 

1.032 

i 

5.59 

(441)   = 

0.14  4 

0.09  4 

3.87 

4.10 

1.362 

Violet     .  .  . 

8.09 

(434)   — 

0.04  — 

0.23  4 

-  3.87 

3.68 

2.197 

G  Bl 

Fig.  162. — Color-curves  of  Maxwell. 


Vi, 


THE  COLOR  SENSE  307 

of  the  different  colors  of  the  spectrum,  and  the  position  of  the 
three  points  in  which  the  curves  cut  the  vertical  line  correspond- 
ing to  each  of  the  colors,  indicates  the  quantities  of  the  three 
standard  colors  needed  to  produce  the  mixture. 

The  negative  sign  of  the  blue,  in  the  equation  of  the  orange, 
is  found  again  for  the  greater  number  of  the  colors  added  to 
one  or  other  of  the  standard  colors.  Its  significance  is  easy  to 
grasp.  In  fact,  if  we  write  the  equation  of  the  orange  thus : 

2.04  Or  -f  0.01  Bl  =  2.36  E  -f  0.74  G 

it  indicates  that  we  cannot,  with  the  three  standard  colors,  pro- 
duce a  mixture  exactly  like  orange,  but  must,  on  the  contrary, 
add  a  little  blue  to  the  orange  so  that  it  may  be  like  the  mixture 
of  red  and  green. 

It  should  be  noted  that,  up  to  the  present,  I  have  simply  ex- 
pressed the  quantity  of  a  color  by  the  width  in  millimeters  of 
the  slit  giving  access  to  this  color.  To  construct  the  table  of 
colors  we  do  the  same  for  the  three  standard  colors;  but  for 
other  colors  we  will  be  obliged  to  select  the  units  in  another 
manner.  I  have  said,  indeed,  that  with  Newton  the  quantity 
of  a  mixture  is  considered  as  equal  to  the  sum  of  the  quantities 
of  the  component  colors.  The  sum  of  the  three  component 
colors  of  the  orange  was 

2.36  -f-  0.74  —  0.01  =  3.09 

while  the  width  of  the  slit  was  2.04  mm.  According  to  Newton, 
the  quantity  of  orange  passing  through  the  slit  of  2.04  mm.  is, 
therefore,  3.09,  that  is  to  say,  the  unit  of  the  orange  corresponds 
to  a  width  of  the  slit  of  ^  =0.662  mm. 

3.09 

If  we  wish  to  use  the  table  to  solve  questions  of  mixtures 
of  colors  we  must,  therefore,  multiply  the  quantities  found  by 
the  table  by  the  figures  indicating  the  units,  in  order  to  obtain 
a  result  expressed  by  the  width  of  the  slit  in  millimeters.  The 
units  are  in  the  last  column  of  the  table.  They  are  obtained  by 
dividing  the  coefficients  on  the  left  by  the  figures  in  the  column 
before  the  last,  which  indicate  the  sum  of  the  component  colors. 


308 


PHYSIOLOGIC  OPTICS 


To  construct  the  spectral  curve,  we  begin  by  drawing  the 
dotted  equilateral  triangle  of  figure  163.  We  suppose  the  three 
standard  colors  placed  at  the  three  angles,  an  arrangement  which 
was  proposed  by  Young.  To  find  the  position  of  the  orange, 
we  begin  by  dividing  the  red-green  side  into  two  parts,  in  the 
proportion  of  0.74  :  2.36.  Let  P  be  the  point  of  division:  join 


Yellow 


eo  y/ 


Bluish-Green 


White 


•?*' 

L' 


Red 


/        Purple 
Fig.  163. — Color  table  of  Maxwell. 


Blue 
Violet 


this  point  to  the  blue  angle  by  a  straight  line,  of  which  we  mea- 
sure the  length  a.  The  color  at  P  can  be  considered  either  as  a 
mixture  of  2.36  R  with  0.74  G,  or  as  a  mixture  of  3.09,  or  with 
o.oi  Bl.  It  follows  that  the  orange  must  be  placed  on  the  pro- 
longation of  a,  beyond  the  point  P,  and  by  designating  its  dis- 
tance from  P  by  x  we  should  have  x=w±a.  This  distance  is, 

3.09 

for  the  orange,  so  small  that  it  is  scarcely  visible  on  the  figure, 


THE  COLOR  SENSE  309 

the  curve  coinciding  at  this  position  almost  with  the  dotted  line. 
— We  observe  that,  on  account  of  the  presence  of  the  negative 
coefficient,  the  color  in  question  must  be  placed  outside  of  the 
triangle.  A  color  which  is  situated  in  the  interior  of  the  triangle 
may  be  reproduced  exactly  by  a  mixture  of  the  three  standard 
colors;  this  is  not  possible  for  a  color  situated  outside  of  the 
triangle:  it  is  necessary,  on  the  contrary,  to  mix  it  with  one  of 
the  standard  colors,  in  order  that  it  may  seem  equal  to  the  mix- 
ture of  the  two  others. 

On  the  table  of  Maxwell  the  greater  part  of  the  spectrum 
(from  0.63  p,  in  the  orange-red  to  0.53  p,  in  the  green,  and 
from  0.51  ^  in  the  green  to  0.47  p,  in  the  blue)  is  arranged  on 
the  two  sides  of  a  triangle  of  which  the  green,  between  0.53  p, 
and  0.51  p,,  forms  a  rounded  angle,  while  the  extremities  of  the 
spectrum  form  two  other  somewhat  irregular  angles.  We  must 
imagine  the  third  side  of  the  triangle  occupied  by 'the  purple 
colors,  which  are  obtained  by  mixing  red  with  blue.  As  nearly 
all  the  spectral  colors  have  one  of  the  coefficients  negative, 
almost  the  entire  curve  is  situated  outside  of  the  triangle  of 
the  standard  colors,  which  indicates  that  the  mixture  colors  have 
nearly  all  a  little  less  purity  than  the  spectral  colors.  The  part 
situated  between  the  red  and  the  green  coincides,  however,  very 
nearly  with  the  corresponding  side.  By  selecting  another 
standard  color,  green,  we  could  make  the  part  of  the  curve 
situated  between  0.51  p,  and  0.47  p,  coincide  with  the  other  side 
of  the  triangle,  but  it  is  easy  to  see  that  we  cannot  select  the 
green  color  so  as  to  make  the  two  sides  coincide  with  the  curve 
at  once.  We  cannot,  therefore,  select  three  spectral  colors  such 
that  we  can  reproduce  all  the  other  spectral  colors  exactly  by 
their  mixtures;  we  can  reproduce  all  the  hues,  but  some  of  the 
mixture  colors  always  continue  to  have  less  purity  than  the 
corresponding  spectral  colors,  whatever  may  be  the  standard 
colors  we  have  chosen. 

By  means  of  the  table  of  Maxwell  we  can  construct  the  re- 
sult of  mixtures  of  any  colors.  If  we  mix  two  colors  placed 
on  the  same  side  of  the  approximately  triangular  curve,  we  ob- 
tain a  mixture  color  which  has  as  much  purity  as  the  spectral 


310  PHYSIOLOGIC  OPTICS 

color,  while  if  we  mix  two  colors  situated  each  on  a  different 
side,  we  obtain  a  mixture  strongly  diluted  with  white.  The 
three  colors  which  Maxwell  selected  as  standard  colors,  the  red, 
green  and  blue,  have,  therefore,  this  peculiarity  that  they  cannot 
be  reproduced  by  mixing  other  spectral  colors,  the  mixture  being 
always  strongly  diluted  with  white. — The  approximately  tri- 
angular form  of  the  curve,  with  the  three  colors,  red,  green  and 
blue,  placed  at  the  angles,  does  not  depend  on  the  choice  of  the 
standard  colors.  By  means  of  the  equations  of  Maxwell,  we 
can,  by  a  simple  calculation,  express  all  the  spectral  colors  by 
three  colors  other  than  his  standard  colors,  for  example  by 
orange,  blue-green  and  blue.  The  curve  even  then  retains  its 
approximately  triangular  form,  having  the  red,  green  and  blue 
at  the  angles,  but  it  differs  considerably  from  the  equilateral 
triangle  formed  by  the  straight  lines  joining  the  three  new 
standard  colors,  which  indicates  that  the  mixture  colors  have, 
in  this  case,  very  little  purity.  Maxwell  selected  red,  green  and 
blue,  so  that  the  curve  would  come  as  near  the  triangle  in  form 
as  possible. 

Contrary  to  what  has  taken  place  in  the  case  of  these  three 
colors,  those  which  are  placed  on  each  of  the  two  sides  of  the 
triangular  curve,  may  be  reproduced  exactly  by  mixing  other 
spectral  colors.  They  are,  in  this  regard,  analogous  to  the  purple 
colors  which  are  obtained  by  mixing  the  red  and  spectral  blue, 
and  which  appear  to  the  eye  as  pure  as  the  pure  spectral  colors. 

The  most  interesting  phenomenon  among  the  great  number 
of  facts  which  are  expressed  by  the  table  of  Maxwell,  is  cer- 
tainly this,  that  we  can  produce  a  perfect  sensation  of  yellow  by 
mixing  red  and  green.  The  fact  was  already  known  to  Young, 
and  formed  the  principal  basis  of  his  theory  of  colors,  which  I 
shall  mention  later  on.  Lord  Raleigh  had  constructed  a  special 
instrument  for  determining  the  quantities  of  spectral  red  and 
spectral  green  necessary  to  produce  a  complete  equality  with 
spectral  yellow.  In  his  numerous  examinations  he  could  always 
obtain  a  perfect  equality,  but  in  the  matter  of  the  quantities 
required  of  the  component  colors,  he  found  quite  unexpected 
individual  differences  (see  page  315).  We  can  also  mix  the 


TEE  COLOE  SENSE  311 

light  of  the  lithium  and  thallium  flames  so  as  to  obtain  a  light 
which  cannot  be  distinguished  from  that  of  the  sodium  flame. 
Another  method,  also  pointed  out  by  Lord  Raleigh,  consists  in 
looking  through  a  liquid  which  allows  only  red  and  green  rays 
to  pass  (a  mixture  of  bichromate  of  potash  and  blue  aniline 
dissolved  in  water).  By  observing  through  this  liquid  an  object 
of  a  bright  white,  a  cloud  illuminated  by  the  sun  for  example, 
it  appears  of  a  pure  yellow,  although  all  the  yellow  rays  are 
completely  absorbed. — The  liquid  is,  besides,  very  sensitive  to 
tints  of  white  light;  the  light  of  the  blue  sky,  which  contains 
too  little  red,  appears  greenish,  while  the  light  of  an  arc  lamp 
appears  reddish. 

The  yellow  occupies  a  special  position  among  the  colors.  An 
observer  completely  ignorant  of  the  results  of  the  mixtures,  as  well 
as  those  of  the  physicists  who  obtain  yellow  by  mixing  spectral 
red  and  green,  as  those  of  the  painters  who,  with  their  pigments, 
obtain  green  by  mixing  yellow  with  blue,  would  probably  be 
temped  to  class  the  yellow  among  the  three  standard  colors  of 
Maxwell,  so  as  to  reckon  four  principal  colors  in  the  spectrum: 
red,  yellow,  green  and  blue.  As  we  have  seen,  the  yellow  is  dis- 
tinguished from  the  three  others  in  that  it  can  be  reproduced 
by  a  mixture  of  other  colors.  In  this  respect  it  is  analogous 
to  the  colors  which  are  placed  on  the  other  sides  of  the  triangle, 
the  purple  and  the  blue-green,  and  it  is  distinguished  from  the 
latter  in  this  that  the  eye  may  not  perceive  any  trace  of  red 
or  green  in  the  yellow,  while  no  one  would  hesitate  to  declare 
that  he  saw  blue  and  red  in  the  purple,  or  green  and  blue  in 
the  blue-green.  The  yellow,  in  this  regard,  resembles  white  in 
which  the  eye  no  longer  distinguishes  any  trace  of  the  compo- 
nent colors.  The  yellow  is  also  that  one  of  the  spectral  colors, 
which,  to  the  eye,  seems  to  offer  most  resemblance  to  white. — 
Another  peculiarity  of  the  yellow,  on  which  Herschel  laid  stress, 
is  the  considerable  change  which  this  color  undergoes  when  its 
brightness  diminishes.  A  dark  blue  still  seems  blue,  while  a 
dark  yellow  appears  brown,  a  color  which  the  observer  not 
prejudiced  would  consider  rather  as  a  special  color. 


312  PHYSIOLOGIC  OPTICS 

We  can  obtain  the  impression  of  white  in  many  different  ways. 
The  celebrated  experiment  by  which  Newton  combined  by  means 
of  a  lens  all  the  colored  rays  of  the  spectrum  in  a  white  image 
shows,  in  the  first  place,  that  all  the  colors  of  the  spectrum, 
when  mixed,  give  white.  The  equations  of  Maxwell  furnish  a 
long  series  of  examples  of  the  possibility  of  forming  white  by 
mixing  three  colors.  Lastly  the  table  indicates  a  great  number 
of  pairs  of  complementary  colors,  that  is  to  say,  colors  which, 
mixed  two  by  two  in  the  proper  proportions,  give  white.  To 
find  the  color  complementary  to  a  given  color,  we  have  only  to 
prolong  the  line  which  joins  it  to  the  white,  yntil  it  meets  the 
curve  again.  The  point  of  intersection  is  the  place  of  the  com- 
plementary color,  and  the  quantities  to  take  of  both  colors  are 
inversely  proportional  to  their  distances  from  the  white.  We 
must  recollect,  however,  that  if  we  wish  to  express  the  quantity 
by  the  width  of  the  slit  in  millimeters,  we  must  reduce  the 
numbers,  as  already  pointed  out. 

A  glance  at  the  table  shows  that  the  green  colors  (greenish) 
from  57  to  49.5  have  no  complementary  colors  in  the  spectrum. 
Their  complementaries  are  the  purple  colors.  The  complemen- 
taries  of  the  red  extremity,  up  to  61,  are  situated  very  near 
one  another  (from  49.5  to  49.2),  those  of  the  blue  extremity 
are  condensed  near  57.  The  hue  varies,  therefore,  very  slowly 
towards  the  extremities  of  the  spectrum,  while  the  variation 
reaches  its  greatest  rapidity  in  the  blue-green,  where  the  di- 
visions are  separated  by  very  marked  intervals. 

Maxwell  did  not  determine  the  extreme  parts  of  the  spectrum ; 
one  might  think,  therefore,  that  the  curve  ought  to  be  really 
more  extended;  but,  according  to  the  researches  of  Kcenig  and 
Dieterici,  this  is  not  the  case.  These  authors  made  a  long  series 
of  very  minute  researches,  like  those  of  Maxwell,  with  their 
large  spectral  instrument.  Their  results  seemed  to  agree  well 
with  those  of  the  latter  author;  however,  they  could  not  verify 
the  bend  which  the  curve  of  Maxwell  makes  in  the  red.  Ac- 
cording to  these  authors,  the  hue  does  not  vary  in  the  spectrum 
beyond  67  and  43,  so  that  the  divisions  beyond  these  limits 
must  on  the  table  coincide  with  these  limits.  Maxwell,  indeed, 


TEE  COLOR  SENSE  313 

himself  calls  the  form  of  the  extremities  of  the  curve  somewhat 
doubtful. 

If  we  compare  the  complementary  quantities  of  red  and  blue- 
green,  we  notice  that  the  red  appears  darker  than  the  green. 
To  illustrate  facts  of  this  kind  on  the  table,  Helmholts  supposed 
as  equal  quantities  of  two  different  colors  quantities  appearing 
to  have  the  same  brilliancy.  He  thus  obtained  the  spectral  curve 
illustrated  in  figure  164.  The  small  circle  indicates  the  position 
of  the  white.  Since  the  red  complementary  to  the  blue-green 

Green 

Yellow 


Red 
Violet*^-  -  Purple 

Fig.  164.— Color  table  of  Helmholts. 

appears  darker  than  the  latter,  we  consider  its  quantity  as 
smaller  and  place  it  consequently  farther  from  the  white.  In- 
deed, such  a  comparison  of  the  brightness  of  two  different  colors 
is  not  easy,  as  Helmholts  himself  remarked,  and  the  result  de- 
pends besides  on  the  phenomenon  of  Purkinje.  If,  for  example, 
a  certain  quantity  A  of  yellow  light  appears  to  have  the  same 
brightness  as  the  quantity  B  of  blue  light,  we  find  that  the 
quantity  -A.  of  yellow  light  will  appear  darker  than  the  quantity 
JL  of  blue  light.  The  form  of  the  curve  would  vary,  therefore, 
according  to  the  brightness  used. 

Maxwell  showed  how,  without  the  help  of  a  spectral  instru- 
ment, we  can  make  determinations  analogous  to  his  own  by 
means  of  the  revolving  disc  of  Masson.  It  is  necessary  to  have 
paper  discs  (colored,  whites  and  blacks)  of  two  different  sizes, 
so  as  to  be  able  to  make  two  mixtures  at  once,  by  covering  the 
central  part  of  the  large  disc  with  the  small  ones. 

We  cut  the  discs  along  a  radius,  in  order  to  be  able  to  com- 
bine them  so  as  to  obtain  colored  sectors  of  any  angle.  We 
select  three  standard  colors,  the  red,  green  and  blue,  and  we 


314  PHYSIOLOGIC  OPTICS 

combine  three  large  discs  so  as  to  have  a  sector  of  each  color. 
In  the  middle  we  place  two  small  discs  combined  so  as  to  have 
a  black  and  a  white  sector.  Making  the  whole  rotate,  we  obtain 
in  the  middle  a  gray  circle,  surrounded  with  a  ring  tinted  with 
the  mixture  of  three  standard  colors.  By  regulating  the  angles 
of  the  sectors  we  make  the  two  tints  alike,  and  write  the  equa- 
tion as  thus: 

165  E  -f-  122  G  -f-  73  Bl  =  100  W  +  260  B  (Aubert) 

W  denotes  the  white,  B  the  black,  and  the  numbers  indicate 
the  angles  of  the  sectors.  Neglecting  the  little  light  reflected 
by  the  black,  we  may  write : 

165  E  -f  122  G  -f-  73  Bl  =  100  W 

To  express  any  other  color,  the  yellow  for  example,  by  the 
standard  colors  we  replace  the  red  sector  by  a  sector  of  this 
color.  Regulating  the  size  of  the  sectors,  we  find  for  example : 

146  Y  -f-  17  G  -f  197  Bl  =  159  W  -f  201  B 
or,  by  dividing  by  1.59, 

92  Y  -f  11  G  -f  124  Bl  =  100  W 

We  then  combine  this  equation  with  that  of  the  standard 
colors,  which  gives 

92  Y  -f  11  G  -f-  124  Bl  =  165  E  -f  122  G  -f-  73  Bl 
or 

1  Y— 1.97  B-f-1.21  G— 0.55  Bl 

With  these  equations  we  can  construct  graphic  illustrations 
of  the  same  kind  as  figures  160  and  162,  and,  by  always  working 
with  the  same  kind  of  papers,  we  may  thus  study  and  compare 
the  color  sense  of  different  eyes ;  but  the  spectral  method  always 
remains  superior. 


THE  COLOR  SENSE  315 

109.  Abnormal  Trichromasia. —  If  we  examine  a  certain  num- 
ber of  persons  by  the  method  of  Maxwell,  on  constructing  the 
color  table  of  each  person,  we  often  find  small  differences:  a 
mixture  which  one  observer  declares  like  white,  seems  to  an- 
other colored.  It  is  probable  that  these  differences  are  due, 
at  least  in  part,  to  the  fact  that  a  portion  of  the  rays  is  absorbed 
by  the  media  of  the  eye,  and  that  this  absorption  is  more  pro- 
nounced in  some  persons  than  in  others.  Thus  the  yellowish 
color  of  the  crystalline  lens  of  old  persons  indicates  that  it  must 
absorb  a  part  of  the  blue  rays.  A  mixture  of  yellow  and  blue, 
which,  to  a  normal  person,  appears  equal  to  the  white,  must 
appear  yellowish  to  the  old  person,  whose  crystalline  lens  absorbs 
relatively  more  of  the  light  of  the  mixture  than  of  the  white 
light.  After  extraction  of  a  cataract,  the  patient  often,  at  the 
first  moment,  affects  to  see  all  blue,  almost  as  everything  appears 
tinted  with  the  complementary  color  when  we  have  looked  for 
a  little  while  through  a  colored  glass  and  then  remove  it  suddenly. 
Maxwell  attributed  some  of  the  phenomena  in  question  to  the 
absorption  of  the  green-blue  rays  by  the  yellow  pigment  of  the 
macula.  Looking  at  a  bright  line  through  a  prism,  he  observed 
a  dark  spot  corresponding  to  the  fovea,  which  moved  up  and 
down  with  the  look,  as  long  as  the  latter  remained  in  the  blue 
part  of  the  spectrum,  but  which  disappeared  as  soon  as  the  look 
left  the  blue.  He  recommended  also,  in  order  to  observe  the 
phenomenon,  fixing  a  yellow  paper  for  a  little  while,  and  then 
transferring  the  look  to  a  blue  paper.  The  spot  then  appears 
for  some  moments.  Taking  two  equal  whites,  one  made  of 
ordinary  white  light  and  the  other  of  a  mixture  composed  in 
great  part  of  green-blue  rays,  the  latter,  seen  in  indirect  vision, 
seemed  greenish  and  more  luminous  than  the  former. 

We  have  seen,  (page  238)  that  the  existence  of  the  yellow 
pigment  of  the  macula  may  appear  doubtful,  but  the  fact  that 
the  macula  is  less  sensitive  to  blue  than  the  remainder  of  the 
retina  is  unquestionable.  I  do  not  see  the  scotoma  in  the  blue 
part  of  the  spectrum,  but  another  observation  which  I  have 
made  is  equally  convincing.  There  exist  in  commerce  trans- 
parent sheets  of  colored  gelatine  which  may  often  with  advantage 


316  PHYSIOLOGIC  OPTICS 

replace  the  colored  glasses  in  many  experiments.  I  have  such 
a  sheet,  tinted  probably  with  an  aniline  color,  which  allows  the 
red  and  blue  rays  to  pass.  When,  looking  at  the  sky,  I  put 
this  sheet  before  my  eye,  I  see  at  the  point  fixed  a  somewhat 
diffuse  red  spot,  almost  the  size  of  the  moon  or  a  little  larger. 
After  an  instant  it  disappears;  if  then  I  remove  the  sheet  with- 
out changing  the  direction  of  the  look,  I  see  the  after-image  of 
the  spot,  very  slightly  greenish  and  clearer  than  the  surround- 
ing parts. — The  color  table  of  Maxwell  himself  differs  some- 
what from  that  of  Mrs.  Maxwell,  illustrated  in  figure  160,  dif- 
ferences which  could  very  well  be  due  to  the  fact  that  inferiority 
of  the  macula  for  the  blue  was  more  pronounced  in  him  than 
in  her. 

Neglecting  these  slight  differences,  an  equation  of  color  which 
is  true  for  a  normal  eye,  remains  true  for  all  eyes  as  well  for 
normal  eyes  as  for  dichromatic  eyes. 

This  latter  assertion  was  considered  entirely  general,  until 
Lord  Rayleigh,  in  1880,  discovered  a  class  of  eyes  for  which  it 
is  not  true.  After  having  produced  a  mixture  of  spectral  red 
and  spectral  green  which  appeared  to  him  identical  with  spectral 
yellow,  he  asked  a  certain  number  of  people  to  compare  the 
two  hues.  Most  of  them  found  the  hues  identical,  but  some, 
amongst  whom  were  his  three  brothers-in-law,  declared  that  they 
saw  scarcely  any  resemblance;  the  pure  color  appeared  yellow 
to  them,  while  the  compound  color  seemed  to  them  nearly  as 
red  as  sealing  wax.  To  see  the  hues  alike,  these  persons  had 
to  add  so  much  green  to  the  mixture  that  it  appeared  nearly 
pure  green  to  a  normal  eye.  The  mixture  of  Lord  Rayleigh 
was  3.13  R-f-i.oo  G;  that  of  his  brother-in-law  1.5  R+i.o 
G.  (i) 

The  persons  in  question  presented  no  other  anomalies  of  the 
chromatic  system ;  they  were  by  no  means  dichromatics  ( dalton- 
ists).  Later  researches  (Bonders,  Kcenig  and  Dieterici)  con- 
firmed the  opinion  of  Lord  Rayleigh  that  these  people  formed  a 


(1)  The  numbers  are  not  comparable  with  those  of  Maxwell,  Lord  Rayleigh 
having  probably  used  colors  different  from  the  standard  colors.  Otherwise  Max- 
well and  Mrs.  Maxwell  would  both  have  belonged  to  the  category  of  abnormal 
trichromasia,  which  is  not  at  all  probable. 


THE  COLOR  SENSE  317 

group  by  themselves:  no  intermediary  forms  have  been  found 
between  their  anomaly,  which  Kcenig  called  abnormal  trichro- 
masia,  and  the  normal  chromatic  system.  The  anomaly  seems 
almost  as  frequent  as  dichromatism ;  Koenig  and  Dieterici  found 
three  cases  of  it  among  seventy  persons  examined,  but  no  case 
is  known  in  which  the  anomaly  was  discovered  by  the  person 
himself  who  was  affected. 

110.  Color-Blindness  or  Dichromasia  (Daltonism). —  The  most 
prevalent  form  of  dyschromatopsia  is  called  daltonism  after  the 
celebrated  English  chemist,  Dalton,  who  was  affected  with  it, 
and  who  gave  the  first  fairly  exact  description  of  it.  It  is  cal- 
culated that  about  4  per  cent,  of  men  are  affected  with  this 
anomaly;  it  is  much  rarer  in  women,  especially  in  its  complete 
form. 

For  the  daltonists,  there  is  in  the  spectrum  a  place,  in  the 
green-blue,  the  color  of  which  resembles  white  (gray).  We 
call  this  place  the  neutral  point.  Instead  of  the  great  variation 
which  the  normal  eye  perceives  in  the  spectrum,  the  daltonists 
see  only  two  colors :  one  which  they  most  frequently  call  yellow, 
and  which  fills  the  entire  part  situated  between  the  neutral  point 
and  the  red  extremity,  and  the  other  which  they  call  blue,  and 
which  extends  from  the  neutral  point  to  the  violet  extremity. 
In  no  part  belonging  to  either  of  the  colors  does  the  hue  change ; 
there  are  differences  of  purity  and  brightness  only.  The  color 
called  yellow  seems  to  them  pure  in  the  red,  orange,  yellow  and 
green,  until  about  0.54^  or  0.53^  near  the  line  E.  In  all  this 
part  there  are  differences  of  brightness  only;  we  can  make  one 
of  these  colors  like  any  other  color  by  changing  the  brightness. 
The  red  and  orange  of  the  spectrum  are  often  so  feeble  that 
they  are  not  perceived  unless  the  spectrum  is  very  clear.  Start- 
ing from  the  line  E,  the  color  becomes  more  and  more  grayish, 
and  at  the  neutral  point  in  the  neighborhood  of  0.50^  (see  fig. 
165)  the  color  is  like  gray.  The  brightness  diminishes  at  the 
same  time;  generally,  the  daltonists  tell  you  that  the  parts 
situated  near  the  neutral  point  are  darker  than  those  situated 
at  some  distance  away  from  it.  It  is  possible  that  this  diminu- 


318  PHYSIOLOGIC  OPTICS 

tidn  of  brightness  is  due  to  the  fact  that  the  neutral  point  is 
situated  in  the  green-blue  part  of  the  spectrum,  the  rays  of 
which  are  most  affected  by  the  influence  of  absorption  in  the 
yellow  pigment  of  the  macula,  a  phenomenon  which  often  seems 
very  pronounced  in  the  dichromatics.  Starting  from  the  neutral 
point  the  other  color  called  blue  begins  to  make  itself  felt :  gain- 
ing in  purity,  it  becomes  pure  at  about  0.46^,  and,  starting  from 
this  point,  presents  differences  of  brightness  only;  the  maxi- 
mum is  near  the  place  where  trie  color  becomes  pure. 

The  dichromatics  see,  therefore,  in  the  spectrum  only  two 
colors,  but  it  is  difficult  to  tell  which.  If  we  designate  the 
colors  as  yellow  and  blue,  it  is  not  a  sure  sign  that  the  spectral 
colors  give  them  the  same  impressions  as  those  which  we  ob- 
tain by  yellow  and  blue.  Generally  speaking,  it  is  impossible 
to  communicate  to  any  one  the  nature  of  a  sensation  which  we 
experience  otherwise  than  by  a  comparison.  If,  for  example, 
one  man  told  another  that  an  object  had  a  sugary  taste,  he  only 
means  to  convey  that  the  object  gives  him  a  sensation  similar 
to  that  which  sugar  would  give  him.  The  other  can  then  verify 
this  if  he  also  finds  that  the  taste  of  the  object  is  similar  to 
that  of  sugar,  and  if  he  finds  it  so  he  will  say  that  the  former 
has  a  normal  taste;  but  it  is  impossible  to  tell  whether  the  object 
has  the  same  taste  for  both. — As  we  cannot  know  how  the 
daltonists  see  colors,  Bonders  proposed  to  replace  in  their  case 
the  expressions  of  yellow  and  blue  colors  by  those  of  warm 
and  cold  colors,  terms  which  are  in  use  among  painters. 

We  must  observe,  however,  that  while  in  all  other  known 
cases  the  daltonism  was  bilateral,  there  exists  in  literature  a 
unique  case  of  uniocular  daltonism ;  it  is  clear  that  such  a  patient 
would  be  well  qualified  to  give  information  on  the  question  of 
knowing  how  the  daltonists  see  the  colors.  The  case  was  very 
well  investigated  by  Hippel.  The  left  eye  was  normal,  while 
the  right  eye,  which  squinted,  but  which  had  been  operated  on 
and  presented  no  ophthalmoscopic  lesion,  showed  an  anomaly 
wholly  analogous  to  ordinary  daltonism.  The  neutral  point 
(situated  at  0.512^)  divided  the  spectrum  into  a  yellow  part 
and  a  blue  part.  The  red  and  green  of  the  spectrum  were,  in 


THE  COLOR  SENSE 


319 


hue,  similar  to  the  yellow,  but  appeared  a  little  less  bright.  Now, 
looking  at  the  yellow  sodium  line,  first  with  one  eye  and  then 
with  the  other,  the  subject  declared  that  the  appearance  was 
the  same  for  both  eyes,  apart  from  a  slight  diminution  of 
brightness  for  the  dichromatic  eye.  It  was  the  same  for  the 
blue  indium  ray  as  for  the  white.  If,  therefore,  we  can  con- 
sider the  case  of  Hippel  as  a  case  of  true  daltonism  the  difficulty 


Green 


52 


56) 


41, 

Yellow       A 


Ovaa^ 


Bluish-Green 


'White 


Red 


/      Purple 

Fig.  165. — Color  table  of  Maxwell. 


Blue 
Violet 


seems  solved.  The  sensations  which  the  daltonists  designate 
as  yellow  and  blue  would  be  identical  with  those  of  normal 
persons. 

As  color-blind  persons  recognize  the  equation  of  the  normal 
eyes,  the  colors  which  are  complementary  for  normal  eyes  are 
also  complementary  for  them.  It  follows  that  the  color  comple- 


320  PHYSIOLOGIC  OPTICS 

mentary  to  the  neutral  point  must  also  appear  gray  to  them 
(or  be  invisible),  as  well  as  all  the  colors  situated  on  the  dia- 
meter of  the  table  which  joins  them.  As  the  colors  next  to 
the  neutral  point  appear  strongly  mixed  with  white,  their  com- 
plementaries,  as  long  as  they  are  in  the  spectrum,  must  appear 
of  very  little  brightness,  since  they  must  neutralize  only  the  little 
chromatic  value  which  is  in  these  grayish  colors. 

While  an  equation  of  colors,  which  is  true  for  a  normal  eye, 
is  so  also  for  the  color-blind,  the  reverse  is  not  true :  color-blind 
persons  recognize  as  similar,  mixtures  which  are  by  no  means 
so  for  a  normal  eye.  For  a  daltonist,  we  can  reproduce  the  im- 
pression of  any  color  of  the  spectrum,  as  well  as  that  of  white, 
by  mixtures  of  two  colors.  On  account  of  this  peculiarity,  the 
anomaly  in  question  is  also  termed  dichromasia. 

Maxivell  used  two  of  his  standard  colors,  green  and  blue.  He 
thus  found,  for  a  dichromatic  student,  the  equation 

4.28  G  +  4.20  Bl  =  W. 

The  position  of  this  mixture  color  is  marked  on  the  table 
(fig.  165)  by  the  letter  k;  the  letter  K  indicates  the  correspond- 
ing spectral  color,  which  is  the  neutral  point.  As  the  daltonists 
recognize  the  equations  of  the  normal  eyes,  we  can  combine  this 
equation  with  that  of  the  normal  eye  (page  305) 

2.36  E  -j-  3.99  G  -f  3.87  Bl  =  W. 
We  have,  therefore,  for  the  daltonist 

2.36  E  -j-  3.99  G  -f-  3.87  Bl  =  4.28  G  -f  4.20  B1 
an  equation  which  we  can  also  write 

L  =  2.36  E  —  0.29  G  —  0.33  Bl  =  0. 

This  latter  color  would  not,  therefore,  produce  any  impres- 
sion on  the  dichromatic  eye  and  would  represent,  up  to  a  certain 
point,  the  element  which  is  wanting  in  it.  Its  place  is  marked 
by  the  letter  L  on  the  table  (fig.  165).  As  L  is  situated  outside 


THE  COLOR  SENSE 


321 


the  spectral  curve,  it  is  a  fictitious  color  which  really  does  not 
exist,  but  which  we  must  suppose  still  purer  than  the  correspond- 
ing spectral  color  which  is  marked  I,  since  it  is  situated  farther 
from  the  white  than  the  latter.  Compared  with  L,  /  is  to  be 
considered  as  a  mixture  of  white.  Nor  is  it  wholly  invisible, 
but  very  feeble. 

For  his  daltonist,  Maxwell  succeeded  in  reproducing  all  the 
colors  of  the  spectrum  by  mixtures  of  his  two  standard  colors. 
The  results  are  represented  by  the  curves  in  figure  166.  More- 


JP1  I  "VL 

Fig.  166. — Color  curves  of  a  dichromatic,  after  Maxwell. 

over,  it  would  be  simpler  to  select  two  colors  which  appear  pure 
to  the  daltonists,  as  van  der  Weyde  and  latterly  Kcenig  and 
Dieterici  have  done.  The  green  color  of  Maxwell  seemed  to 
the  daltonists  slightly  mixed  with  gray,  as  the  curves  show. 


51 


Fig.  167. — Color  table  of  a  dichromatic,  after  the  measurements  of 
Koenig  and  Dieterici. 

On  the  table  of  colors  the  whole  chromatic  system  of  the 
daltonists  is  reduced  to  a  straight  line  (fig.  167),  since  all  the 
colors  which  we  can  produce  by  mixing  two  given  colors  must 
be  placed  on  the  straight  line  which  joins  them.  The  line,  too, 


322  PHYSIOLOGIC  OPTICS 

corresponds  only  to  the  part  of  the  spectrum  in  which  the  colors 
are  seen  mixed  with  white,  because  all  the  parts  where  the 
colors  seem  pure,  must  come  together  in  the  two  points  which 
form  the  extremities  of  the  line. 

Examining  a  series  of  daltonists,  we  observe  that  the  position 
of  the  neutral  point  is  not  exactly  the  same  in  all.  It  varies 
in  different  persons  between  0.492^  and  0.502^.  In  figure  165 
these  two  points  are  marked  R  and  S;  it  is,  therefore,  between 
R  and  S  that  the  position  of  the  neutral  point  may  vary,  and 
consequently,  the  direction  of  the  neutral  diameter  would  vary 
between  RT  and  SQ.  There  results  a  certain  difference  between 
daltonists  whose  neutral  point  is  situated  nearer  R,  and  those 
in  whom  it  is  situated  nearer  S.  In  the  former,  the  neutral 
diameter  passes  through  the  green-blue  and  the  red  (i),  and 
the  spectrum  seems  shortened,  because  the  red  extremity  con- 
tains the  colors  complementary  to  the  grayish  colors  and  must, 
consequently,  as  we  have  seen,  appear  very  dark.  In  the  others, 
the  neutral  point  corresponds  to  a  color  situated  nearer  the 
green,  the  complementary  of  which  is  purple,  and  not  found 
in  the  spectrum.  As  the  colors  complementary  to  the  gray 
parts  of  the  spectrum  do  not  correspond  to  the  red  extremity, 
the  latter  preserves  its  ordinary  intensity  and  the  spectrum  is 
not  seen  shortened. 

Guided  especially  by  theoretical  considerations  (see  page  329), 
it  has  been  proposed  to  distinguish  between  these  two  forms 
by  designating  the  former  as  anerythropsia  (Rothblindheit) ,  the 
latter  as  achloropsia  (Grunblindheit).  It  was  Seebeck  who 
first  distinguished  between  these  two  forms;  but  although  he 
has  been  followed  by  a  great  number  of  scientists,  among  others 
by  HelmholtZf  Holmgren,  Leber  and  Kcenig,  this  distinction  does 
not  yet  seem  completely  justified.  If  the  neutral  diameter  had 
always  either  the  direction  SQ  or  the  direction  RT,  it  would  be 


(1)  In  order  not  to  depart  from  the  terminology  which  is  generally  used,  I 
have  designated  the  colors  from  0.62  to  0.63^  as  reds,  but  it  must  be  noted  that 
with  the  division  of  the  spectrum  which  I  have  adopted  in  figure  151,  and  which 
was  proposed  by  Listing,  these  colors  are  already  in  the  orange.  On  the  other 
hand,  Chibret  found  with  his  instrument  that  the  colors  which  the  daltonists  con- 
found most  frequently  are  the  orange  and  blue. 


THE  COLOE  SENSE  323 

reasonable  to  distinguish  between  the  two  forms,  but  there  seem 
to  exist  intermediary  forms.  The  position  of  the  neutral  point 
is,  moreover,  not  constant,  even  for  the  same  individual:  it  is 
displaced  a  little  towards  the  blue  when  we  increase  the  bright- 
ness of  the  spectrum  (Preyer). 

There  have  been  described  some  very  rare  cases  of  anomalies 
of  color  vision,  which  are  usually  classified  under  the  name  of 
akyanopsia  (Blaublindheit).  In  these  cases  the  neutral  point 
would  be  found  in  the  yellow-green,,  and  the  spectrum  would 
be  seen  shortened  at  its  blue  extremity.  But  the  existence  of 
this  form  is  far  from  being  established.  In  cases  of  poisoning 
with  santonine,  we  meet  anomalies  of  color  vision  which  are 
somewhat  in  accord  with  these  observations,  but  these  phe- 
nomena seem  rather  to  be  attributed  to  a  slight  transient  colora- 
tion of  the  vitreous  body. 

In  consequence  of  the  deficiency  of  their  chromatic  system, 
the  daltonists  are  often  exposed  to  errors,  which  are  especially 
striking  when  they  confound  red  with  green.  This  is  why 
Dalton  used  to  walk  in  the  street  with  the  scarlet  cloak  of  the 
Oxford  doctors,  thinking  that  it  was  black  or  gray.  Cherries 
seem  to  them  of  the  same  color  as  the  leaves  of  the  cherry 
tree,  etc.  To  understand  these  errors  we  must  recollect  that 
the  colors  of  objects  are  never  pure;  they  always  contain  white, 
and  this  is  why  red  objects  appear  gray  and  not  almost  black 
like  the  red  of  the  spectrum.  In  spite  of  these  errors  it  is  often 
astonishing  to  see  how  the  daltonists  know  how  to  overcome 
their  defect  by  making  use  of  the  differences  which  the  colors 
present  to  them.  Comparing,  for  example,  red  with  yellow, 
they  can  frequently  give  their  true  names  to  these  colors.  The 
hue  for  both  is  the  same,  but  the  red  appears  to  them  less  pure 
than  the  yellow,  and  they  know  that  this  less  pure  yellow  is 
what  is  generally  called  red.  They  generally  seem  more  sensi- 
tive to  differences  of  brightness  than  normal  persons  do,  and 
they  can  sometimes  see  traces  of  color  which  the  normal  eye 
does  not  discover.  Thus  Mauthner  relates  a  case,  in  which  the 
daltonist  claimed  that  he  saw  yellow  on  a  sheet  of  black  paper. 
On  examining  the  paper  it  was  found  that  it  really  did  reflect 


324  PHYSIOLOGIC  OPTICS 

a  little  of  the  yellow  light,  which  had  escaped  the  normal  ob- 
server. 

111.  Monochromasia. —  There  exists  yet  another  anomaly  of 
the  color  sense,  which  is  very  rare,  but  seemingly  well-estab- 
lished, name  monochromasia.     While  color-blindness  implies  no 
other  abnormality,  mono-chromatic  eyes  manifest  all  other  signs 
of  weakness :   photophobia,  albinism,   diminution  of  the  visual 
acuity,  etc.     For  these  people  differences  of  color  do  not  exist; 
the  only  differences  they  perceive  are  differences  of  brightness, 
almost  as  on  an  engraving.     The  whole  color  table  is  narrowed 
to  a  point.     The  spectrum  seems  to  them  simply  a  luminous 
band,  the  brightness  of  which  reaches  its  maximum,  not  in  the 
yellow  as  is  the  case  with  the  normal  eye,  but  in  the  green  (at 
about  0.52^,).    Hering  emphasized  the  analogy  which  exists  be- 
tween the  manner  in  which  monochromatics  see  the  spectrum, 
and  the  appearance  which  it  presents  to  the  normal  eye  when 
its  brightness  is  very  feeble. 

112.  Clinical  Examination  of  the  Color  Sense. — The      method 
of  mixing  colors  forms  the  fundamental  examination  of  the  color 
sense,  and  we  can  scarcely  pass  it  over  if  we  desire  to  form  an 
exact  idea  of  the  chromatic  system  of  the  person  whom  we 
observe;  but  the  method  is  too  complicated  for  clinical  use,  and 
it  is,  besides,  completely  dependent  on  the  good   faith  of  the 
person  whom  we  examine.     For  the  clinician  it  is  important  to 
be  able  to  decide  quickly  and  surely  whether  his  client  is   a 
dichromatic  or  not.    With  this  object  in  view  different  methods 
have  been  invented. 

It  must  first  be  noted  that  we  obtain  only  little  useful  in- 
formation by  asking  a  color-blind  person  how  he  would  term 
the  color  of  such  and  such  an  object.  If  we  present  red  to  him, 
for  example,  it  may  not  unlikely  happen  that  he  will  designate 
this  color  as  red,  although  he  does  not  see  it  different  from 
certain  greens. 

The  method  most  used  is  the  test  with  colored  yarns  (Holm- 
gren). We  present  to  the  subject  the  green  shade  of  least  purity 


THE  COLOR  SENSE  325 

and  we  request  him  to  find  the  shades  which  resemble  the  latter, 
adding  that  they  may  be  a  little  more  or  a  little  less  pronounced. 
Besides  the  green  shades,  the  daltonist  matches  yellow  grays, 
brown  grays,  red  grays  and  pure  grays.  We  then  present  to  him 
pure  purple.  It  is  here  that  the  alleged  difference  between  the 
two  kinds  of  daltonists  becomes  apparent.  A  person  affected 
with  anerythropsia  would  find  that  the  blue  and  violet  hues 
resemble  pure  purple,  while  a  person  affected  with  achloropsia 
would  select  the  green  and  gray  shades.  Individuals  who  have 
only  an  incomplete  color-blindness  would  stand  the  latter  test, 
but  not  the  former.  Krenchel,  Daae  and  others  arranged  colored 
yarns  in  the  form  of  charts;  Cohn  used  colored  powders:  See- 
beck,  who  invented  the  method,  used  colored  papers. 

On  the  tables  of  Stilling  are  arranged  a  great  number  of 
spots  of  two  colors,  selected  so  as  to  be  seen  alike  by  the  dalton- 
ist. There  are,  for  example,  on  one  sheet  complementary  spots, 
red  and  green;  the  reds  are  arranged  between  the  greens  so  as 
to  form  numbers  visible  to  the  normal  eye,  but  invisible  to  the 
dichromatic  eye,  which  sees  all  the  spots  of  the  same  color. 
The  tables  of  Stilling  do  not  seem  very  good;  it  appears  that 
there  are  daltonists  who  read  them,  and  normal  eyes  which  do 
not  read  them.  The  tables  of  Pfliiger,  which  I  have  already  men- 
tioned, are  preferable;  they  are  based  on  a  phenomenon  of  con- 
trast. The  patient  looks  at  a  purple  sheet  on  which  are  printed 
gray  letters;  the  whole  is  covered  with  tissue  paper.  A  normal 
eye  sees  the  purple  ground  through  the  tissue  paper,  and  easily 
reads  the  letters  which  appear  by  contrast  in  the  complementary 
color.  The  daltonist  sees  the  ground  gray  like  the  letters,  so 
that  he  cannot  distinguish  the  latter. 

We  can  prove  that  the  anomaly  is  not  feigned  by  making  the 
patient  look  through  a  colored  glass.  If  the  patient  confounds 
green  and  red  he  should  no  longer  confound  them  when  look- 
ing through  a  red  glass,  for,  as  the  green  rays  do  not  pass 
through  this  glass,  the  green  must  appear  to  him  much  darker 
than  the  red.  Daltonists  who  need  to  be  able  to  distinguish 
colors,  chemists  for  example,  may  sometimes  use  with  advantage 


326  PHYSIOLOGIC  OPTICS 

a  colored  glass,  which  puts  them  in  a  position  to  distinguish  be- 
tween two  colors  which  they  otherwise  confound. 

Polarization  instruments  have  been  used  to  discover  color- 
blindness; Rose  constructed  the  first  instrument  of  this  char- 
acter; the  leucoscope  of  Koenig  is  founded  on  the  same  principle. 
The  best  <of  these  instruments  is  the  chromatoptometer  of 
Chibret.  If  we  place  a  plate  of  quartz  cut  parallel  to  the  axis 
between  two  Nicols,  parallel  to  each  other  and  forming  an  angle 
of  45°  with  the  axis  of  the  quartz,  we  see  the  plate  tinted  a 
certain  color  which  depends  on  the  thickness  of  the  quartz. 
Making  the  Nicol  nearest  the  eye  (the  analyzer)  rotate  around 
the  axis  of  the  tube,  the  color  becomes  less  and  less  pure.  At 
45°  the  field  is  white,  and  if  we  continue  to  rotate  the  Nicol  we 
obtain  the  complementary  color,  which  increases  the  purity,  up 
to  90°,  when  it  attains  its  highest  point.  Replacing  the  analyzer 
by  a  double  refracting  crystal,  a  plate  of  spar,  for  example, 


ESL 


Fig.  168. — Chromatoptometer  of  Chibret. 

which  acts  like  two  Nicols,  perpendicular  to  each  other,  the 
field  is  seen  double  and  one  of  the  images  of  the  field  has  the 
color  complementary  to  that  of  the  other.  Rotating  the  spar. 
the  colors  become  less  and  less  pure,  and  at  45°  the  two  fields 
are  white.  The  hues  of  the  two  complementary  colors  depend 
on  the  thickness  of  the  plate  of  quartz.  In  the  instrument  of 
Chibret,  by  placing  the  plate  more  or  less  obliquely,  we  can 
use  a  greater  or  less  thickness,  and  thus  obtain  the  whole  gamut 
of  colors.  The  instrument  thus  presents  a  very  great  number 
of  hues  and  degrees  of  purity. 


THE  COLOR  SENSE  327 

The  patient  looks  towards  a  window  through  the  instrument. 
We  place  the  index  of  purity  ES  (fig.  168),  which  regulates  the 
position  of  the  doubly  refracting  crystal,  at  5°,  which  gives 
colors  strongly  mixed  with  white,  and  after  having  put  the 
index  of  the  hues  E  G,  which  regulates  the  inclination  of  the 
quartz  on  the  orange,  at  zero,  we  ask  the  patient  if  the  fields 
are  alike.  If  they  are  not,  we  rotate  the  index  of  the  hues 
slowly  towards  the  red,  yellow  and  violet.  If  the  patient  al- 
ways sees  the  two  fields  different  we  repeat  the  experiment 
after  having  placed  the  index  of  purity  at  zero,  which  makes 
the  two  fields  white.  He  ought  now  to  see  them  alike.  If  the 
patient  stands  these  tests,  he  is  not  color-blind.  If,  on  the  con- 
trary, in  the  first  experiment  he  sees  the  two  fields  alike  for 
a  certain  hue,  he  is  color-blind.  We  then  increase  more  and 
more  the  purity  of  these  hues.  If  we  thus  succeed  in  producing 
a  difference  between  the  two  fields  the  daltonism  is  incomplete; 
in  the  contrary  case,  it  is  complete. 

If  there  is  question  of  persons  who  desire  a  certificate  to  be 
employed  on  railroads,  or  as  sailors,  etc.,  it  may,  in  addition, 
be  useful  to  examine  whether  they  can  distinguish  signals.  An 
aperture  of  3  millimeters  diameter  in  a  screen,  covered  with 
white  paper,  and  illuminated  from  behind  by  a  lamp,  suffices 
for  this  examination.  We  place  the  person  to  be  examined  at 
5  or  6  meters  distance,  and  we  see  whether  he  commits  errors 
when  we  place  glasses  of  different  colors  before  the  aperture. 

113.  Hypotheses  on  the  Mechanism  of  Color  Vision.  —  To  ex- 
plain the  mechanism  of  color  vision  different  hypotheses  have 
been  tried:  the  old  ones  were  without  any  anatomical  basis; 
the  more  recent  have  been  more  or  less  inspired  by  the  discovery 
of  the  retinal  purple.  None  of  these  hypotheses  are  satisfactory 
in  character,  and  the  facts  known  up  to  the  present  do  not 
seem  yet  sufficient  to  explain  the  mechanism  of  color  vision.  Let 
us  mention  briefly  these  hypotheses. 

THEORY  OF  YOUNG. — The  following  is  how  Young  explained 
his  hypothesis:  "It  is  certain  that  we  can  produce  a  perfect 
sensation  of  yellow  and  blue  by  a  mixture  of  green  and  red 


328  PHYSIOLOGIC  OPTICS 

light  and  of  green  and  violet  light.  There  are  reasons  for 
supposing  that  these  sensations  are  always  composed  of  a  com- 
bination of  separate  sensations.  This  supposition  at  least  sim- 
plifies the  theory  of  colors;  we  may,  therefore,  accept  it  with 
advantage  until  such  time  as  we  shall  find  it  incompatible  with 
some  phenomenon.  We  shall  proceed,  therefore,  to  consider 
white  light  as  composed  of  a  mixture  of  three  colors  only,  red, 
green  and  violet." 

According  to  this  hypothesis,  we  suppose  each  nervous  fibre 
of  the  retina  composed  of  three  fibres  of  the  second  order;  each 
of  these  three  fibres  would  be  provided  with  a  special  terminal 
organ  (a  photo-chemical  substance)  and  also  with  a  special 
central  organ.  An  irritation  of  the  first  fibre  would  produce  a 
red  sensation,  an  irritation  of  the  second  fibre  a  green  sensation 
and  an  irritation  of  the  third  a  violet  sensation.  These  three 
colors  are  termed  principal  colors.  An  irritation  of  the  first 
two  fibres  would  produce  yellow,  etc.  An  irritation  at  once 
of  the  three  fibres  produces  white,  and  if  none  of  the  fibres  is 
irritated,  we  have  the  sensation  of  black.  The  red  rays  irritate 
the  first  fibre,  the  green  rays  the  second,  the  violet  rays  the 
third;  the  yellow  rays  irritate  the  first  and  second,  and  so  forth. 
Young  explained  color-blindness  by  supposing  that  one  of  the 
fibres  was  wanting. — One  of  the  advantages  of  this  hypothesis 
is  that  we  can  suppose  the  action  identical  in  the  three  fibres. 
The  action  in  the  terminal  organs  must  necessarily  be  different, 
but  the  one  in  which  the  impression  is  conducted  to  the  brain 
may  be  the  same  in  the  three  cases.  The  difference  between 
the  three  sensations  would  be  produced  by  the  different  reaction 
of  the  central  organs. 

In  this  form  the  theory  is  very  attractive,  but  does  not  ac- 
cord with  observations  on  color  vision.  It  requires,  indeed, 
that  we  can  select  three  spectral  colors  so  as  to  be  able  to  re- 
produce all  existing  hues  and  degrees  of  purity  by  mixing  them. 
But  we  have  seen  that  this  is  not  possible;  there  always  remain 
some  of  the  spectral  colors  which  are  purer  than  the  mixtures. 
According  to  Young  the  color  table  must  have  an  exactly  tri- 
angular form,  but  the  observations  of  Maxwell  have  shown  that 


THE  COLOS  SENSE  329 

this  is  not  the  case.  We  cannot  use,  for  example,  the  standard 
colors  of  Maxwell  as  principal  colors,  because  we  cannot  repro- 
duce with  them  the  colors  situated  outside  of  the  triangle. 

MODIFICATION  OF  THE  THEORY  OF  YOUNG  BY  HELMHOLTZ. — 
We  must,  therefore,  suppose  that  the  sensations  corresponding 
to  the  principal  colors  are  still  purer  than  the  spectral  colors, 
for  then  their  mixtures  could  have  the  same  purity  as  the  latter. 
On  the  table  the  principal  colors  would  then  be  placed  farther 
from  the  center  than  the  spectral  colors,  so  that  the  triangle, 
which  we  would  obtain  by  joining  them,  would  complete  the 
entire  curve. 

Helmholtz  supposed  that  each  spectral  color  irritated  the  three 
fibres  at  once,  but  in  a  different  degree.  Thus  the  red  rays 
would  irritate  the  first  fibre  strongly,  the  other  two  feebly.  The 
impression  produced  by  the  spectral  red  would  already  contain 
white.  Helmholtz  remarked,  in  this  regard,  that  this  impression 
is  not  the  purest  sensation  of  red  that  we  can  have.  If  we  first 
produce  an  after-image  of  an  object  of  the  complementary  color, 
before  looking  at  the  spectral  red,  the  impression  becomes  much 
more  vivid,  because  we  would  thus  have  fatigued  the  two  other 
fibres. 

Helmholtz  at  first  tried  to  explain  color-blindness,  as  Young 
did,  by  the  absence  of  one  of  the  fibres.  He  supposed,  there- 
fore, three  kinds  of  color-blindness:  anerythropsia,  achloropsia 
and  akyanopsia.  As  we  have  seen,  the  last  form  is  very  doubt- 
ful, and  the  first  two  seem  to  become  blended  into  one.  But, 
there  are  yet  other  difficulties.  Persons  who  are  color-blind 
declare  that  they  see  yellow  or  blue  in  the  spectrum,  while,  ac- 
cording to  Helmholtz,  they  should  see  green  and  violet  or  red 
and  violet.  The  hypothesis  was  saved  by  saying  that  it  was 
not  possible  to  know  what  they  meant  to  convey  by  blue  and 
yellow,  but  as  this  explanation  became  very  doubtful,  after  the 
observation  of  Hippel,  the  hypothesis  was  modified  once  more 
by  supposing  that  color-blind  persons  possess  three  fibres,  but 
that  in  them  the  colors  act  equally  on  two  of  the  fibres.  If,  for 
example,  the  red  rays  act  as  much  on  the  first  as  on  the  second 
fibre,  they  must  produce  a  yellow  sensation.  It  is  the  same  for 


330  PHYSIOLOGIC  OPTICS 

green  rays.  Taking  the  blue  as  the  third  principal  color,  we 
could  thus  explain  the  manner  in  which  color-blind  people  see 
the  colors;  but  all  these  modifications  do  not  add  to  the  plausi- 
bility of  the  hypothesis. 

THEORY  OF  HERING. — This  scientist  assumes  a  "visual  sub- 
stance" which  is  a  mixture  of  three  others:  one,  which  deter- 
mines the  sensation  of  black  and  white,  another,  which  deter- 
mines that  of  red  and  green,  and  a  third,  which  determines  that 
of  yellow  and  blue.  The  red  light  acts  on  the  red-green  sub- 
stance, causing  a  katobolic  change  (disassimilation)  which  pro- 
duces the  sensation  of  red.  The  green  light,  on  the  contrary, 
would  cause  an  anabolic  change  in  this  substance  by  its  action 
(assimilation)  which  would  produce  the  sensation  of  green.  The 
same  takes  place  in  the  case  of  the  yellow  and  blue  rays  in  re- 
lation to  the  yellow-blue  substance.  The  intermediary  rays  act 
on  the  two  substances  alike.  But  all  the  rays  acts  on  the  whitish- 
black  substance,  which  Hering  expresses  by  saying  that  these 
rays  have  besides  their  color  value  (Volenz),  a  white  value 
( Valenz)  also.  It  is  not  only  the  white  light,  but  also  the  colored 
rays,  which  disassimilate  this  substance.  If  the  two  other  sub- 
stances did  not  exist,  all  the  rays  would  produce  a  white  sen- 
sation, but  of  different  brightness.  This  is  what  takes  place  in 
the  case  of  monochromatics  (achromatics).  If  only  one  of  the 
two  substances  is  wanting  we  have  the  dichromatic  system. 

Hering  supposes,  therefore,  four  principal  colors:  red  and 
green,  yellow  and  blue,  and  he  thinks  that  we  have  a  direct  im- 
pression of  the  fact  that  these  four  colors  are  pure,  and  that 
the  others,  perceived  by  an  action  on  the  two  substances  together, 
are  compound. 

The  rivalry  between  these  two  theories,  the  first  of  which 
was  inspired  by  observations  on  mixtures  of  colors,  whilst  the 
second  seems  to  be  derived  especially  from  the  study  of  after 
images,  has  formed  the  subject  of  a  great  number  of  works; 
the  pupils  of  Helmholtz  tried  to  prove  that  the  hypothesis  of 
Hering  was  false,  and  vice  versa.  It  seems  to  me  that  both 
theories  have  suffered  by  it.  The  theory  of  Hering  seems  rather 
to  give  a  statement  of  known  facts,  than  to  explain  them.  It 


THE  COLOR  SENSE  331 

is  based  on  the  fact,  which  it  seems  to  me  difficult  to  deny,  that 
the  human  eye  does  not  see  any  resemblance  between  the  four 
principal  colors  of  the  spectrum,  red,  yellow,  green  and  blue, 
while  each  of  the  intermediary  colors  resembles  two  of  the  prin- 
cipal colors.  But  it  must  be  noted  that  the  red  of  Hering  ought 
to  be  complementary  to  the  green ;  it  does  not  correspond,  there- 
fore, to  the  spectral  red,  which,  according  to  Hering,  already 
contains  yellow,  but  to  a  purple  color  which  we  cannot  readily 
claim  to  give  the  direct  impression  of  a  pure  color,  (i)  It 
seems  to  me  also  that  a  theory  which  renders  no  account  of 
the  special  situation  of  the  yellow  among  the  colors,  is  necessarily 
insufficient. 

OTHER  THEORIES. — Among  the  more  recent  theories,  we  may 
cite  that  of  Ebbinghaus,  who  supposes  the  existence,  in  the  cones, 
of  a  green  substance,  the  decomposition  of  which  would  produce 
the  sensation  of  red  and  green,  while  the  purple,  by  its  decom- 
position, would  produce  the  sensation  of  yellow  and  blue. 
Parinaud  supposes  that  stimulation  of  the  rods  produces  a  sen- 
sation of  non-colored  light,  while  stimulation  of  the  cones  may 
produce  all  possible  sensations,  the  sensation  of  colors  and  the 
sensation  of  white.  The  retina  would  have  two  systems  sensi- 
tive to  light,  one  monochromatic,  the  other  trichromatic.  The 
ideas  of  v.  Kries  almost  agree  with  those  of  Parinaud. 

Arthur  Kcenig  exploited  a  theory  which  may  be  considered 
as  a  development  of  the  theory  of'  Young-Helmholtz.  He  sup- 
poses the  red,  green  and  blue  as  principal  colors.  According  to 
Kcenig,  the  decomposition  of  the  retinal  purple  into  yellow  pro- 
duces the  weak  sensation  of  gray,  which  causes  any  color  when 
it  is  sufficiently  weak.  Further  decomposition  produces  the  sen- 
sation of  blue.  Perception  of  the  two  other  principal  colors, 
green  and  red,  is  effected  by  the  agency  of  the  pigment  cells, 
while  the  cones  must  be  considered  as  dioptric  instruments  in- 


(1)  Towards  the  periphery  of  the  visual  field  there  exists  a  dichromatic  zone, 
in  which  we  see  only  yellow  and  blue  colors.  A  red  object  seems  yellow  at  this 
place,  while  a  purple  color  appears  blue;  it  is  the  intermediary  tint  which 
corresponds  to  the  red  of  Hering. 


332  PHYSIOLOGIC  OPTICS 

tended  to  concentrate  the  light  on  the  epithelial  layer. — I  have 
already  mentioned  that  H..  Muller  measured  the  distance  of  the 
retinal  vessels  from  the  sensitive  layer  by  means  of  the  parallax 
of  the  vessels,  seen  entoptically  (see  page  183).  In  collabora- 
tion with  Zumft,  Kwnig  repeated  these  experiments  with  spectral 
light.  He  found  that  the  distance  increases  according  as  we 
approach  the  red  end  of  the  spectrum.  The  layer  sensitive  to 
green  light,  and  especially  that  sensitive  to  red  light,  would, 
therefore,  be  situated  behind  the  layer  sensitive  to  blue.  The 
distance  of  these  two  layers  exceeded  even  the  retinal  thickness, 
which  led  Koenig  to  suppose  that  the  perception  of  these  two 
colors  takes  place  in  the  epithelial  layer. — These  experiments 
still  need  to  be  verified;  Koster  repeated  them  without  success. 

Bibliography. — In  spite  of  the  great  number  of  works  on  color  vision, 
this  question  still  seems  imperfectly  elucidated.  In  the  preface  to  his 
treatise  on  light  which  appeared  a  few  years  before  Newton's  works  on 
optics,  Huyghens  said  he  would  not  speak  of  colors,  "a  question  in  which, 
up  to  the  present,  no  one  can  pride  himself  on  his  success. "  It  seems 
to  me  that  this  phrase,  which  was  true  at  the  time  of  Huyghens  as  to  the 
physics  of  colors,  may  be  applied  to-day  to  their  physiology.  This  subject 
has  not  yet  found  its  Newton. 

Newton  (I.).  Optics.  London,  1704. — Lambert.  Farbenpyramide.  Augs- 
burg, 1772. — Dalton,  Edinburgh.  PMlos.  Journal.  Vol.  VI. — CEuvres  de 
Young,  edited  by  Tscherning,  p.  217-232. — Purkinje.  Zur  Physiologic  der 
JSinne.  II,  p.  109,  1825. — Seebeck.  Ueber  den  bei  manchen  Personen  vor- 
Icommenden  Mangel  an  Farbensinn.  Pogg.  Ann.,  1837,  p.  177. — Helm- 
holtz  (H.).  Ueber  die  Theorie  der  zusammengesetzten  Farben.  Pogg.  Ann., 
1852,  p.  45. — Helmholtz  (H.).  Ueber  die  Zusammensetzung  der  Spectral- 
farben.  Pogg.  Ann.,  1855,  p.  1. — Helmholtz  (H.).  Ueber  die  Empfindlich- 
Tceit  der  menschlichen  NetzJiaut  fur  die  brechbarsten  Strahlen  des  Sonnen- 
lichts.  Pogg.  Ann.,  1855,  p.  205. — Maxwell  (C.).  Experiments  on  Colors 
as  Perceived  by  the  Eye  with  Remarks  on  Color  Blindness.  Transact,  of 
the  Eoy.  Soc.  of  Edinb.,  XXI,  1855.— Maxwell  (C.).  On  the  Theorie  of 
Compound  Colors  and  the  Relations  of  the  Colors  of  the  Spectrum.  Phil, 
trans.,  1860. — Maxwell  (C.).  On  the  Unequal  Sensibility  of  the  Foramen 
Centrale  to  Light  of  Different  Colors.  Edinb.  Journ.,  1856,  IV,  p.  337. — 
Hering  (E.)  in  Lotos  Prag.,  1880-82-85-87. — Kayleigh.  Nature.  Vol.  XXV, 
p.  64,  1881. — Mace  de  Lepinay  and  Nicati.  Ann.  de  chimie  et  de  physique. 
6er.  5,  t.  24,  p.  289,  1881  et  t.  30,  p.  145,  1883.— Uhthoff  (W.).  Ueber 
das  Abhdngiglceitsverhaltniss  der  Selischdrfe  von  der  Beleuchtungsintensitdt. 
Grafes  Arch.  XXXII,  1886. — Uhthoff  (W.).  Weitere  Untersuchungen  ilber 
die  AbhdngigTceit  der  Sehschdrfe  von  der  Intensitdt  sowie  von  der  Wellen- 


THE  COLOR  SENSE  333 

lange  im  Spelctrum.  Grafes  Arch.  XXXVI,  1890. — Kriess  (I.  v.).  Die 
Gesichtsempfindungen  und  ihre  Analyse.  Leipzig,  1882. — v.  Hippel.  Grafes 
Archiv.  XXVII,  3,  p.  47,  1881.— Krenchel  (W.).  Ueber  die  Hypothesen 
von  Grundfarben.  Grafes  Arch.  XXVI,  p.  91,  1880. — Kcenig  u.  Brodhun. 
Experimentelle  Untersuchungen  fiber  die  psychophysische  Fundamental- 
formel  in  Bezug  auf  den  Gesichtssinn.  Acad.  of  Berlin,  July  26,  1888,  and 
June  27,  1889. — Kcenig  (A.)  and  Dieterici  (C.).  Die  Grwidempfindungen 
in  normalen  und  anomalen  Farbensystemen  und  ihre  Intensitdtsverthelung 
im  Spectrum.  Zeitschrift  fur  Psychol.,  IV,  p.  241,  1892. — Ktaenig  (A.)  et 
Zumft  (I.).  Ueber  die  lichtempfindliche  Schlicht  in  der  Netzhaut  des  men- 
schlichen  Auges.  Acad.  of  Berlin,  1894,  May  24. — Kcenig  (A.).  Ueber  den 
menschlichen  Sehpurpur  und  seine  Bedeutung  fur  das  Sehen.  Acad.  of 
Berlin,  1894,  June  21. — Chibret.  Chromatoptometre.  Bulletin  de  la  Soc. 
fr.  d'opht.,  1886,  p.  336. — Ebbinghaua  (H.).  Theorie  des  Farbensehens. 
Hamburg,  1893. — Parinaud  (H.).  La  sensibilite  de  Voeil  aux  couleurs 
spectrales;  fonctions  des  elements  retiniens  et  du  pourpre  visuel.  Ann.  d'oc. 
t.  CXII,  p.  228,  1894. — Koster  (W.).  Ueber  die  percipirende  Schicht  der 
Netzhaut  beim  Menschen.  Grafes  Arch.,  LXI,  1,  p.  1,  1895. 


CHAPTER  XVIII 
THE  FORM  SENSE 

114.  Central  Visual  Acuity. —  The  power  of  distinguishing 
forms  is  a  very  complex  faculty,  which  is  in  great  part  con- 
nected with  the  ocular  movements.  To  judge  of  the  form  of 
objects  we  grope  for  them,  so  to  speak,  with  the  look.  Never- 
theless, indirect  vision  furnishes  an  idea  of  the  form  of  objects. 
According  to  empiric  ideas  (page  263)  it  would  be  the  observa- 
tions made  during  the  displacements  of  the  look  that  would 
have  taught  us  the  meaning  of  the  impressions  obtained  in  in- 
direct vision. 

The  lowest  angle  under  which  two  points  can  be  distinguished 
from  each  other  has  been  taken  as  the  measure  of  the  form 
sense.  Astronomers  for  a  long  time  devoted  attention  to  this 
question.  Hooke,  for  instance,  said  that  in  order  that  a  double 
star  can  be  recognized  as  such  by  the  eye,  the  interval  must 
correspond  to  one  minute,  and  moreover,  that  good  eyes  would 
be  necessary  to  see  two  stars  under  these  conditions.  Later,  the 
physiologists  took  up  the  question,  generally  by  working  with 
a  small  grating  the  bars  and  intervals  of  which  were  of  the 
same  size.  We  place  the  grating  towards  the  sky  and  try  how 
far  we  can  move  away  from  it  before  the  bars  become  confused. 
Care  must  be  taken  that  the  image  formed  on  the  retina  is  dis- 
tinct, by  correcting  defects  of  refraction,  if  there  are  any.  In 
accord  with  most  observers  Helmholtz  found  nearly  the  same 
angle  as  Hooke,  that  is  to  say,  one  minute,  but  it  must  be  ob- 
served that  it  is  neither  the  width  of  a  bar  nor  that  of  the  in- 
terval, but  the  sum  of  the  two,  which  corresponds  to  this  angle. 

Considering  the  anatomical  structure  of  the  retina,  we  would 
expect  that  the  angle  of  least  distinction  would  correspond  to 
the  size  of  a  cone.  In  the  experiment  of  Hooke  we  may  sup- 
pose, indeed,  that  we  can  distinguish  two  stars  if,  between  the 
two  cones  on  which  their  images  are  formed,  there  is  found  a 

334 


THE  FORM  SENSE 


335 


third,  which  does  not  receive  any  impression  (fig.  169).  We 
may,  therefore,  conclude  that  the  angular  size  of  a  cone  must 
be  smaller  than  the  angular  distance  separating  the  two  stars. 


Fig.   169. 

Experiment  of  HooTce. 
The  images  of  two 
stars  (e,  e)  are  formed 
on  two  cones  separated 
by  a  third. 


Fig.   170. 

Measurement  of  the 
visual  acuity  by  a 
grating. 

aa,  Images  of  the 
bars  separated  by 
those  of  the  intervals, 
fcfc. 


Fig.   171. 

Measurement  of  the 
visual  acuity  with  a 
grating. 

Limit. — All  the  cones 
receive  the  same  im- 
pression. 


In  the  experiment  of  Helmholtz,  on  the  contrary,  we  cannot 
conclude  that  the  size  of  the  cone  must  be  smaller  than  the 
angular  size  of  the  black  bar;  for  we  can  very  well  imagine  a 
larger  cone,  the  central  part  of  which  may  be  occupied  by  the 
image  of  the  black  bar,  while  the  lateral  parts  would  be  occupied 
by  a  part  of  the  images  of  the  intervals,  but  which  would  re- 
ceive, however,  less  light  than  the  neighboring  cones  (fig.  170). 
But  we  can  conclude  that  the  cone  must  be  smaller  than  the 
angular  distance  separating  the  centers  of  the  two  neighboring 
luminous  intervals  (or,  which  amounts  to  the  same  thing,  smaller 
than  the  sum  of  the  black  bar  and  a  luminous  interval),  for  if 
the  size  of  the  cones  were  equal  to  this  distance,  all  the  cones 
would  receive  the  same  quantity  of  light  (fig.  171),  and  the 
bars  would  be  confused.  Thus  the  result  obtained  by  Helmholtz 
is  in  agreement  with  that  of  Hooke. 

Placing  the  distance  of  the  nodal  point  of  the  eye  from  the 
retina  at  15  mm.  the  angular  size  of  a  minute  corresponds  to 

n  =0.004  mm-    In  the  fovea  the  size  of  the  cones  is  about 


ftn     Qgn 

uU  /\  ooU 

0.002  mm.    The  visual  acuity  does  not  seem,  therefore,  to  alto- 


336 


PHYSIOLOGIC  OPTICS 


gather  reach  the  degree  which  we  would  expect  according  to 
the  structure  of  the  retina,  probably  on  account  of  optic  ir- 
regularities. It  seems  rare,  indeed,  that  a  luminous  point  forms 
its  image  on  a  single  cone,  and  if  it  extends  over  several  cones, 
it  is  not  strange  that  the  angle  of  least  distinction  is  larger  than 
the  angular  size  of  a  cone  (fig.  172). 


Fig.  172. — Experiment  of  EooTce,  the  optics  of  the  eye  being  defective. 
Instead  of  distinct  images,  the  stars  form  diffusion  spots,  ee,  ee. 

One  might  think  that  the  least  angle  of  visibility  may  serve 
as  a  measure  of  the  form  sense,  that  is  to  say,  that  we  can 
measure  it  by  determining  what  is  the  smallest  visual  angle  un- 
der which  an  object  may  be  seen;  but  it  is  evident  that  this 
angle  depends  solely  on  the  luminous  intensity  of  the  object, 
for,  in  spite  of  their  minimum  angular  size,  we  see  fixed  stars 
very  well  when  they  are  sufficiently  luminous. 

If  the  eye  were  optically  perfect,  so  that  the  image  of  star 
could  be  formed  on  the  surface  of  a  single  cone,  it  is  easy  to 
see  that  the  luminous  impression  which  this  cone  may  receive, 
if  it  be  sufficiently  strong,  would  suffice  to  make  the  object 
visible,  even  if  the  image  did  not  occupy  the  entire  surface  of 
the  cone.  But,  as  a  rule,  the  optic  properties  of  the  eye  are  not 
so  good.  Most  people  do  not  see  the  stars  as  points,  but  as 
small  surfaces  so  much  greater  in  proportion  as  the  star  is 
brighter;  the  image  of  the  star  is,  indeed,  a  circle  of  diffusion 
composed  of  more  or  less  luminous  parts:  when  the  light  is 
feeble  these  latter  parts  disappear  so  that  the  star  appears 
smaller.  As  long  as  the  star  is  luminous  the  image,  therefore, 
generally  covers  several  cones;  if  the  light  diminishes  the  image 
may  be  formed  on  a  single  cone,  but  the  visibility  always  de- 
pends on  the  brightness  only.  A  comparison  with  the  preceding 


THE  FOEM  SENSE  337 

experiment  shows  also  that  we  cannot  use  the  visibility  of  a 
single  star  as  a  measure  of  visual  acuity;  the  experiment  would 
be  identical  with  that  of  the  grating,  if  we  imagine  two  infinitely 
large  bars  separated  by  an  interval  corresponding  to  the  star. 
We  have  seen  that  we  may  conclude  that  the  angular  size  of 
the  cone  is  smaller  than  the  angular  size  of  a  bar  plus  an  in- 
terval; but  this,  in  the  present  case,  has  no  application. 

In  clinics  we  use,  for  the  measurement  of  visual  acuity,  the 
charts  of  Snellen  or  others  constructed  on  the  same  principle. 
The  letters  are  arranged  so  as  to  be  seen  under  an  angle  of  5 
minutes;  the  lines  which  form  the  letters,  as  well  as  most  of 
the  intervals  which  separate  them,  are  seen  under  an  angle  of 
i  minute.  We  see  that  the  normal  acuity  of  Snellen  corresponds 
to  half  of  that  which  Helmholtz  found,  with  his  grating,  in 
which  each  bar  and  each  interval  corresponded  to  a  half  minute. 
We  have  found  also  that  the  best  eyes  have  a  visual  acuity 
which  approaches  2  (f  or-f)>  and  we  can  be  almost  certain  that 
if,  with  a  good  illumination,  the  acuity  is  only  equal  to  I,  the 
eye  presents  defects  sufficiently  pronounced  to  be  easily  estab- 
lished. 

We  have  said  that  the  angle  under  which  the  letters  are  seen 
corresponds  to  5  minutes.  The  angle  being  equal  to  the  linear 
size  of  the  letter  divided  by  the  distance  at  which  it  is  seen,  it 
is  clear  that  the  letters  which  are  intended  to  be  seen  at  a  dis- 
tance of  12  meters  must  have  double  the  linear  size  of  those 
which  are  seen  at  6  meters.  If  the  former  are  seen  at  a  distance 
of  6  meters  only,  we  say  that  the  visual  acuity  is  equal  to  JL  __L 
Different  authors,  Javal  among  others,  have  observed  that  this 
way  of  designating  the  visual  acuity  is  not  very  logical,  and 
that  we  should,  in  this  case,  say  that  the  acuity  is  equal  to  J, 
since  the  surface  of  the  letter  in  question  is  4  times  greater 
than  that  which  corresponds  to  the  acuity  I. 

In  spite  of  the  theoretical  objections  which  may  be  made  to 
it,  the  chart  of  Snellen  is,  however,  very  practical.  It  is  certain 
indeed,  that  some  of  the  letters  are  much  more  easily  read  than 
others  on  the  same  line.  The  legibility  of  a  letter  is,  indeed,  a 
very  complex  affair,  which  is  far  from  depending  altogether 


338  PHYSIOLOGIC  OPTICS 

on  the  size  of  the  intervals  separating  the  different  lines.  At- 
tempts have  been  made  to  remedy  this,  sometimes  by  making 
larger  the  letters  which  are  read  with  difficulty,  sometimes  by 
selecting  only  letters  which  are  easily  legible.  These  improve- 
ments are  not  widely  employed,  for  they  are  without  much 
utility;  by  using  the  chart  we  learn,  in  fact,  very  quickly  the 
degree  of  legibility  which  each  letter  has  for  a  normal  eye.  A 
more  serious  inconvenience  is  the  small  number  of  large  letters, 
which  frequently  renders  the  determination  of  refraction  diffi- 
cult in  cases  in  which  the  acuity  is  not  so  good,  because  the 
patients  learn  the  letters  by  heart.  To  have  a  constant  illumina- 
tion, it  is  well  to  place  the  chart  in  a  dark  place  and  to  illuminate 
it  with  a  gas  jet  provided  with  a  reflector,  which  protects  the 
eyes  of  the  patient.  The  chart  of  Javal  is  transparent  and  placed 
by  the  side  of  the  patient,  who  looks  at  it  in  a  looking-glass. 
We  thus  achieve  this  result,  that  the  letters,  being  opaque,  are 
always  seen  perfectly  black,  and  that  the  distance  is  double  by 
reflection.  The  size  of  the  letters  increases  in  geometrical  pro- 
gression, which  had  already  been  proposed  by  Green.  Burcardt 
had  printed  series  of  groups  of  dots  of  different  sizes  arranged 
after  the  principle  of  Snellen.  The  patient  must  be  able  to 
count  the  number  of  dots  which  compose  a  group.  Many  oculists 
followed  the  example  of  Snellen  and  constructed  charts  on  the 
same  principle. 

We  still  use  the  reading  test  types  of  Jaeger,  the  first  fairly 
complete  collection  of  characters  of  different  sizes  which  had 
been  used.  The  advantage  which  the  chart  of  Snellen  presents 
is  that  it  has  written  upon  it  the  distance  at  which  the  patient 
ought  to  be  able  to  see  each  line,  which  enables  oculists  to  ex- 
amine the  sight  of  all  patients  at  a  like  distance.  This  principle 
had  already  been  applied  by  Stellwag. 

In  1891,  Guillery  proposed  to  measure  the  visual  acuity  simply 
by  the  distance  at  which  we  can  distinguish  a  black  point  on  a 
white  ground.  By  comparisons  with  the  letters  of  Snellen,  he 
found  that  a  black  point  seen  under  an  angle  of  50  seconds 


THE  FORM  SENSE  339 

corresponds  to  the  normal  acuity;  at  5  meters  it  should  have 
a  diameter  of  1.2  mm.  This  point  is  designated  as  No.  I.  No. 
2  has  the  surface  twice  as  large  as  No.  i,  and  the  patient  who 
sees  only  No.  2  at  5  meters  distance,  has  an  acuity  of  £,  etc. 
Each  point  is  on  a  white  square,  sometimes  in  the  center,  some- 
times below,  sometimes  in  an  angle,  etc.,  and  there  are  on  the 
same  line  several  tests  side  by  side  in  which  the  point  has  the 
same  size.  The  patient  must  tell  at  what  part  of  the  square 
he  sees  the  point.  It  seems  that  we  measure  the  visual  acuity 
quite  as  well  in  this  way  as  by  the  principle  of  Snellen,  which 
is  quite  interesting,  and  shows  that  we  cannot  identify  the  ex- 
aminations with  the  luminous  point  on  a  black  ground  with 
that  made  by  means  of  a  black  point  on  a  white  ground.  Javal 
constructed  a  small  portable  scale  on  the  same  principle:  it  is 
composed  of  small  black  squares,  such  that  the  side  of  a  square 
is  also  equal  to  the  diagonal  of  the  preceding  one.  If  the  side 


is  equal  to  i,  the  diagonal  is  \/i2-f-i2  =  <v/2,  which  is  the  side  of 
the  following  square;  the  diagonal  of  this  latter  is  then  2,  and 
so  forth.  In  this  manner  the  area  of  a  square  is  always  double 
that  of  the  preceding  square. 

RELATIONS  BETWEEN  VISUAL  ACUITY  AND  ILLUMINATION.  — 
The  visual  acuity  depends  directly  on  the  illumination  of  the 
chart,  but  it  is  quite  difficult  to  determine  the  relation  in  a 
general  way,  because  there  are  many  different  factors  which 
affect  it.  Thus  the  relation  must  depend  on  the  pupillary  size, 
on  the  manner  in  which  the  pupil  contracts  under  the  influence 
of  light,  on  the  degree  of  optic  perfection  and  especially  on  the 
adaptation  of  the  eye  to  darkness.  Druault  has  made  some 
researches  on  this  question,  by  moving  a  candle  (of  stearine  of 
22  mm.  diameter)  towards  the  visual  acuity  chart,  and  noting 
the  distance  at  which  this  light  would  allow  each  line  to  be 
read;  the  eye  was  in  a  degree  of  medium  adaptation.  In  order 
to  obtain  high  degrees  of  illumination,  he  replaced  the  candle 
by  a  lamp  equivalent  to  fifty-four  candles.  The  following  table 
shows  his  results,  taking  as  unit  the  illumination  obtained  by 
placing  a  candle  at  a  distance  of  one  meter. 


340  PHYSIOLOGIC  OPTICS 

\ 

Illumination.  Acuity. 

15 

0.016  meter  candles —  =  0.075 

200 
15 

0.020      "  "        —  =  0.15 

100 
15 

0.028      "  "        —  =  0.21 

70 
15 

0.047      "  "        —  =  0.30 

50 
15 

0.12       "  M       —  =  0.37 

40 
15 

0.25       "  "        —  =  0.50  ! 

30 
!  .  15 

0.67        "  "       —  =  0.75 

20 

15  i 

1.50        "  "       —  =  1.00 

p  15  ! 

15 

16.7         "  "        —  =  1.25 

12 
15 

5400  "  "        —=1.50 

10 

We  note  that  the  acuity  increases  rapidly  at  first,  then  slowly, 
with  the  illumination,  and  finally  there  is  need  of  an  enormous 
increase  of  illumination  in  order  to  make  the  acuity  rise  from 
1.25  to  1.50.  Still  increasing  the  illumination,  the  acuity  would 
probably  still  increase,  but  very  little,  so  that  the  curve  indi- 
cating the  visual  acuity  for  the  different  illuminations  would  be 
a  flattened  curve  much  elongated  and  more  or  less  like  the  curve 
of  the  light  sense  (fig.  148). 

I  have  already  observed  that  the  relation  between  the  visual 
acuity  and  the  illumination  depends,  furthermore,  on  the  color 
of  the  light  used  (page  293). 


TEE  FORM  SENSE  341 

The  theory  according  to  which  the  layer  of  the  cones  and 
rods  would  be  the  sensitive  layer,  explains  sufficiently  well  the 
acuity  which  we  obtain  with  a  good  illumination,  but  it  gives 
by  no  means  a  satisfactory  explanation  of  the  manner  in  which 
the  acuity  falls  when  the  illumination  diminishes. 

115.  Peripheral  Acuity. —  We  determine  the  limits  of  the 
visual  field  with  a  perimeter  or  campimeter,  by  allowing  the 
person  examined  to  fix  the  center,  and  finding  up  to  what  limit 
the  patient  can  still  see  the  object  in  indirect  vision.  The  dis- 
tance of  the  eye  from  the  plane  of  the  campimeter,  or  from 
the  arc  of  the  perimeter,  varies  slightly  for  different  instruments. 
The  object  is  generally  a  white  square  (or  a  colored  one),  the 
side  of  which  is  about  I  centimeter.  W!ith  the  white  object 
we  thus  find  the  absolute  limits  of  the  field;  taking  larger  or 
brighter  objects  we  scarcely  obtain  any  more  extended  limits. 
It  is  otherwise  for  the  examination  with  colors.  It  seems,  in- 
deed, that  by  taking  sufficiently  large  and  bright  objects  we 
obtain  larger  limits  than  by  ordinary  examination.  In  clinics, 
we  examine  generally  with  the  white,  blue,  red  and  green,  and 
we  find,  as  a  rule,  the  field  less  extended  in  the  order  in  which 
I  have  named  the  colors.  If  one  finds  different  limits  for  the 
red  and  green,  this  is  probably  due  to  the  fact  that  colors  which 
are  not  complementary  or  which  have  a  different  brightness  are 
used.  Otherwise  we  ought  to  find  the  same  limits. 

The  visual  acuity  falls  greatly  as  soon  as  the  image  is  moved 
away  from  the  fovea.  If,  for  example,  we  fix  the  border  of 
the  chart  of  Snellen  the  acuity  falls  in  consequence  to  -J-  or  A. 
Attempts  have  been  made  to  determine  the  peripheral  acuity 
according  to  the  principle  of  Snellen,  but  the  method  is  very  diffi- 
cult to  use  clinically,  whilst  another  method  introduced  by 
Bjerrum  seems  to  give  good  results.  He  simply  repeats  the 
perimetric  examination  with  smaller  and  smaller  objects.  He 
uses  a  distance  of  2  meters,  placing  the  patient  in  front  of  a 
large  black  curtain;  the  objects  used  are  small  ivory  discs  of 
different  sizes,  fixed  on  black  rods  of  I  meter  in  length.  The 


342  PHYSIOLOGIC  OPTICS 

observer  must  wear  black  gloves.    By  thus  examining,  Bjerrum 
found  as  the  limits  of  the  normal  field: 

Outside.  Inside.  Below.  Above. 

With  a  disk  of 3mm        350  30°         30°         25° 

—         —        6mm         5Qo  4Qo          4Qo          350 

Normal  limits 9Qo  6Qo         7Qo         6Qo 

By  this  method  we  can  frequently  establish  defects  which  we 
could  not  otherwise  find.  We  thus  meet  cases  of  atrophy  of 
the  optic  nerves,  in  which  the  field  examined  in  the  ordinary 
manner  is  normal,  whilst  the  method  of  Bjerrum  reveals  con- 
siderable contractions.  In  glaucoma  Bjerrum  has,  by  his  method, 
discovered  scotomata  scattered  in  the  field,  but  which  are  gen- 
erally connected  with  a  spot  of  Mariotte  by  a  lacuna  in  the  form 
of  a  bridge.  The  paracentral  scotoma  is  thus  connected  with 
the  papilla  by  a  lacuna  which  surrounds  the  upper  or  lower  half 
of  the  macula.  Its  form  indicates  directly  the  course  of  the 
nerves.  Sometimes  it  may  be  useful  to  repeat  the  examination 
with  diminished  illumination. 

More  recently,  Groenouw  has  made  analogous  measurements 
with  a  black  point  on  a  white  ground.  He  designates  as  isopters 
the  lines  drawn  in  the  visual  field  through  the  points  where  the 
visual  acuity  is  the  same.  These  methods  are  founded  on  the 
same  principle  which  was  used  by  Guillery  for  the  measurement 
of  central  acuity.  Their  theory  is  still  to  be  formulated. 

In  the  normal  field  there  is  only  one  interruption,  namely,  the 
blind  spot  which  corresponds  to  the  papilla.  It  was  discovered 
by  Mariotte,  whose  name  it  bears,  and  created  at  the  time  a 
very  great  sensation.  From  his  discovery  Mariotte  drew  this 
conclusion,  that  it  is  the  choroid  which  is  the  sensitive  layer  of 
the  eye,  since  it  was  absent  in  this  place,  and  this  idea  was  for 
a  long  time  accepted.  We  can  determine  the  form  of  the  blind 
spot  by  the  ordinary  methods  with  the  perimeter,  and  still  better 
by  placing  ourselves  at  a  distance  of  one  or  two  meters.  The 
spot  has  an  elliptical  form;  generally  we  succeed,  on  examining 
with  a  very  small  object,  in  following  the  big  vessels  a  little 


THE  FORM  SENSE  343 

outside  of  the  papilla  (fig.  173).  If  we  do  not  succeed  in  follow- 
ing them  farther,  it  is  due  to  the  lack  of  stability  of  the  fixation. 
According  to  the  researches  of  Dr.  Holth,  who  drew  figure  173, 
it  is  almost  impossible  to  maintain  an  almost  exact  fixation  for 
more  than  5  or  6  seconds;  after  this  time  the  look  makes  in- 


Fig.  173. — Marietta's  blind  spot  in  my  right  eye,  drawn  by  Holth. 

voluntary  deviations  which  may  reach  a  third  or  half  a  degree, 
and  after  20  or  30  seconds  we  frequently  observe  deviations 
which  often  exceed  one  degree.  We  can  control  fixation  by 
using  as  the  object  of  fixation  a  point  marked  on  a  small  colored 
surface  on  a  white  ground.  After  a  very  short  time  we  see 
the  surface  surrounded  with  a  border  of  the  complementary 
color. — The  internal  border  of  the  spot  of  Mariotte  is  about  12 
degrees  from  the  point  of  fixation,  and  the  diameter  corresponds 
to  about  6  degrees,  or  12  times  the  diameter  of  the  moon. 

PHENOMENON  OF  TROXLER. — If  we  draw  several  black  spots 
on  a  sheet  of  paper  and  fix  one  of  them  for  some  time,  we  see 
sometimes  one,  sometimes  another  of  the  surrounding  spots  dis- 
appear, to  reappear  a  little  while  after,  generally  at  the  moment 
of  winking  or  of  making  a  slight  movement  of  the  eye.  This 


344  PHYSIOLOGIC  OPTICS 

singular  phenomenon  which  was  described  at  the  beginning  of 
this  century  by  Troxler,  has  recently  been  studied  by  Dr.  Holth. 
The  color  of  the  background,  as  well  as  that  of  the  spots,  plays 
no  part ;  during  the  disappearance  of  these  latter  we  see  in  their 
place  the  background  only;  the  scotoma  is,  therefore,  filled  al- 
most like  the  spot  of  Mario  tie.  Even  the  spot  fixed  may  dis- 
appear after  a  long  period  of  fixation.  In  order  to  study  the 
phenomenon  we  can  observe  a  regular  diagram  as  in  figure  174. 


Pig.  174. 

For  my  eye  the  phenomenon  begins  after  having  fixed  the  middle 
for  8  or  9  seconds,  that  is  to  say,  at  the  moment  when  the  fixa- 
tion begins  to  be  less  steady.  From  this  moment  the  figure 
shows  continuous  changes:  sometimes  one  part  of  the  figure 
disappears,  sometimes  another.  An  interesting  fact  is  that  most 
frequently  the  scotomata  are  not  absolute:  sometimes  it  is  the 
horizontal  lines  which  disappear  at  one  place,  while  the  vertical 
lines  persist,  sometimes  the  contrary  takes  place.  These  phe- 


THE  FORM  SENSE  345 

nomena  recall  forcibly  that  which  has  been  described  under  the 
name  of  antagonism  of  the  visual  fields  and  which  we  observe, 
for  example,  when  presenting  in  a  stereoscope  horizontal  lines 
to  one  eye  and  vertical  lines  to  the  other. — If  we  fix  the  center 
of  a  figure  composed  of  concentric  circles  and  radii,  we  see 
sometimes  the  latter,  sometimes  the  circles.  On  a  chess-board 
we  see  sometimes  one,  sometimes  another  of  the  squares  dis- 
appear, and  so  forth.  Holth  even  caused  luminous  objects  to 
disappear,  the  moon  for  example;  according  to  him  small  ob- 
jects disappear  even  if  we  give  them  a  slow  motion.  There  is 
reason,  therefore,  to  be  on  the  guard  against  this  source  of 
error,  if  we  wish  to  perform  perimetry  with  precision. 

Bibliography. — Hooke  v.  Smith,  Robert.  Cours  complet  d'optique,  trans- 
lated by  Pezenas.  Paris,  1767,  p.  44. — Troxler.  Ueber  das  Verschwinden 
gesehner  Gegenstdnde  innerhalb  unseres  Gesichtslcreises.  Himly  v.  Schmidt. 
Ophthalm.  Bibliothelc.,  1802,  II,  p.  1. — czuvres  de  Young,  edited  by  Tscher- 
ning,  p.  78. — Stellwag  v.  Carion.  Die  Accommodations  fehler  des  Auges. 
Wien,  1855. — Guillery.  Ein  Vorschlag  zur  Vereinfachung  der  Sehproben. 
Arch.  f.  Augenheilk.,  XXIII,  p.  323,  1891. — Grcenouw.  Ueber  die  Sehschdfe 
der  Netzhautperipherie  und  eine  neue  Untersuchungsmethode  derselben. 
Arch.  f.  Augenheilk.,  XXVI,  p.  85,  1893. — Bjerrum.  Undersoegelsen  af 
Synet.  Copenhagen,  1894. — S.  Holth.  Om  det  normale  Synsorgans  Stirre- 
blindhed.  Norsk  Magazin  for  LaegevidenTcaben.  August,  1895. 


BOOK  III 

THE  OCULAR  MOVEMENTS 

AND 

BINOCULAR  VISION 


CHAPTER  XIX 
THE  LAW  OF  LISTING 

116.  Center  and  Axes  of  Rotation  of  the  Eye. — The  movements 
of  the  eye  are  made  freely  in  all  directions;  the  extent  of  the 
field  of  fixation  is  about  55°  in  all  directions. — It  is  easy  to 
prove  that  the  soft  parts  which  fill  the  orbit  are  incompressible: 
if  we  try  to  push  the  eye  backwards,  we  meet  with  considerable 
resistance;  the  movements  of  the  eye  are  limited,  therefore,  to 
its  rotations. 

These  rotations  are  made,  at  least  approximately,  around  a 
center  which,  according  to  the  determinations  of  Danders,  is 
situated  about  10  mm.  in  front  of  the  posterior  surface  of  the 
sclera,  or  14  mm.  behind  the  summit  of  the  cornea.  It  coincides 
with  the  center  of  the  posterior  surface  of  the  globe,  supposed 
to  be  spherical.  It  is  not  certain  that  the  center  of  rotation  is 
exactly  the  same  for  movements  in  different  directions. 

Danders,  in  collaboration  with  Dojer,  determined  the  position 
of  the  center  of  rotation  of  the  eye  in  the  following  manner. 
He  first  measured  the  diameter  of  the  cornea  with  the  ophthal- 
mometer  of  Helmholtz,  and  then  placed  a  hair  (a,  fig.  175) 
stretched  vertically  in  a  ring,  in  front  of  the  middle  of  the 
cornea.  He  then  examined  the  angular  size  of  the  lateral  move- 
ments of  the  look,  which  the  observed  person  had  to  make,  in 
order  that  the  hair  would  be  seen  successively  in  coincidence 

346 


THE  LAW  OF  LISTING 


347 


with  the  left  and  right  borders  of  the  cornea.  Let  ACD  (fig. 
175)  be  one  of  these  movements,  p  half  the  diameter  of  the 
cornea,  and  x  the  distance  CE.  Then  we  have  p=xtg  ACD, 


Fig.  175. 

from  which  we  can  calculate  x.  Adding  to  this  distance  the 
height  of  the  cornea,  we  find  the  distance  of  the  center  of  ro- 
tation from  the  cornea. 


348  PHYSIOLOGIC  OPTICS 

The  six  motor  muscles  form,  as  we  know,  three  pairs,  (i) 
which  cause  the  eye  to  turn  around  three  axes  passing  through 
the  center  of  rotation  of  the  eye.  The  axis  of  the  external  and 
internal  recti  is  vertical.  The  axes  of  the  two  other  pairs  are 
situated  in  the  horizontal  plane.  The  nasal  extremity  of  the  axis 
of  the  superior  and  inferior  recti,  BAi  (fig.  176)  is  situated  a 
little  in  front,  so  as  to  form  an  angle  of  about  70°  with  thef 
visual  line.  The  temporal  extremity  of  the  axis  of  the  oblique 
muscles  CD  (fig.  176)  is  directed  very  much  forwards;  it  forms 
an  angle  of  about  35°  with  the  visual  line. 

The  internal  and  external  recti  turn  the  eye,  therefore,  directly 
inwards  and  outwards.  The  superior  and  inferior  recti  direct 
the  look  upwards  and  downards,  but  at  the  same  time  a  little 
inwards.  The  inferior  and  superior  oblique  direct  the  look  either 
downwards  or  upwards  but  at  the  same  time  outwards.  The 
look  is  directed  straight  upwards  by  the  combined  action  of  the 
superior  rectus  and  the  inferior  oblique,  and  the  direction  down- 
wards is  obtained  by  the  combined  action  of  the  inferior  rectus 
and  superior  oblique. 

The  muscles  make  possible  the  rotation  of  the  globe  around 
any  axis.  This  is  all  that  it  is  of  importance  to  know  for  the 
physiology  of  the  eye.  We  must  not  think  that  the  eye  turns 
oftener  around  the  axes  which  we  have  just  described,  than 
around  the  intermediary  axes.  It  seems,  indeed,  that  all  six 
muscles  are  concerned  each  time  the  eye  makes  any  motion; 
the  axis  around  which  the  eye  turns  is,  therefore,  always  differ- 
ent from  the  three  which  we  have  just  mentioned. 

117.  The  Law  of  Listing. — Supposing  the  head  to  be  motion- 
less, the  position  of  the  eye  is  determined  for  a  given  point  of 
fixation.  This  is  far  from  being  evident  a  priori,  for  the  eye 
could  still  perform  rotations  around  the  visual  line.  Each  time 
that  the  look  returns  to  the  same  point,  no  matter  in  what 


(lj  [This  statement  is  only  approximately  true,  as  according  to  the  careful 
measurements  of  Volkmann,  each  of  the  six  muscles  of  the  eye  seems  to  rotate 
the  latter  around  its  own  axis.  See  paper  by  the  translator  in  the  Archives  of 
Ophthalmology,  Vol.  XXVII,  No.  1,  1898 :  Are  our  present  ideas  about  the 
mechanism  of  the  eye-movements  correct?] — W. 


me 

«i 


THE  LAW  OF  LISTING  349 

way,  the  eye  always  reassumes  the  same  position  (Donders). 
If,  by  fixing  a  colored  ribbon  stretched  horizontally,  we  produce 
an  after  image,  and  then  project  the  latter  on  a  wall,  keeping 
the  head  motionless,  the  image  assumes  a  position  which  is  not 
ways  horizontal,  but  which  is  always  the  same  every  time  that 

look  returns  to  a  given  point.    This  position  is  determined 

he  law  of  Listing. 

here  exists  a  certain  direction  of  the  visual  line  in  relation 
to  the  head,  which  we  call  primary  direction;  the  corresponding 
position  of  the  eye  is  named  primary  position,  and  every  other 
position  (direction)  is  called  secondary.  The  primary  direction 
generally  corresponds  to  the  direction  which  the  visual  line 
assumes  when  we  look  at  the  horizon,  giving  to  the  head  the 
position  which  seems  most  natural;  but  it  happens  quite  fre- 
quently, however,  that  one  is,  under  these  circumstances,  obliged 
to  lower  the  look  slightly,  in  order  to  put  the  eye  in  the  primary 
position.  In  this  case,  one  is  obliged  to  lean  the  head  slightly 
backwards  in  order  to  make  the  primary  direction  horizontal. 
We  must  suppose  this  direction  invariably  connected  with  the 
head,  in  all  the  movements  of  which  it  partakes. 

According  to  the  law  of  Listing,  the  eye  may  be  brought  from 
the  primary  position  to  any  secondary  position  by  a  rotation 
around  an  axis  perpendicular  to  the  two  successive  directions  of 
the  visual  line.  This  defines  for  us  at  the  same  time  the  primary 
position. — The  axes  of  Listing  are  all  contained  in  a  plane  per- 
pendicular to  the  primary  direction  and  pass  through  the  center 
of  rotation  of  the  eye.  This  plane  is,  therefore,  as  invariably, 
connected  with  a  head. 

To  demonstrate  the  law  of  Listing,  we  place  ourselves  at  a 
distance  of  one  or  two  meters  from  a  wall  on  which  is  placed  a 
fixation  mark  A  (fig.  177),  on  a  level  with  the  eyes.  It  is 
necessary  to  make  the  position  of  the  head  secure.  If  we  do 
not  wish  to  make  very  exact  measurements,  a  head-rest,  like 
that  of  the  ophthalmometer  of  Javal  and  Schioets,  suffices.  If, 
on  the  contrary,  we  desire  a  very  great  exactness,  we  use  the 
little  mouth-board  (planchette)  of  Helmholtz,  the  border  of 
which  is  covered  with  sealing  wax.  We  squeeze  the  planchette 


350 


PHYSIOLOGIC  OPTICS 


between  the  teeth  while  the  sealing  wax  is  still  warm,  so  that 
the  latter  may  receive  the  imprint  of  the  teeth.  We  then  fix 
the  planchette  on  a  stand,  so  as  to  be  able  to  turn  it  to  the  right 
or  to  the  left  or  to  incline  it  any  number  of  degrees  fixed  upon 
(Hering). 

We  place  on  the  wall,  at  A,  a  rectangular  cross  so  tha; 
arms  may  be  horizontal  and  vertical.     The  cross  ought  to 
trast  boldly  with  the  background,  so  as  to  permit  us  to  obt" 
a  very  pronounced  after  image  by  fixing  it  for  a  little  while.    We 
take  the  planchette  between  the  teeth  and,  inclining  the  head 


U^J\Jll 

Dtl^^F 


-4"  ------- 


-+ 4- 4- 


Fig.  177. 

(with  the  planchette)  a  little  forward  or  backward,  or  inclining 
it  a  little  to  the  right  or  to  the  left,  we  find  a  position  such  that 
on  moving  the  look  along  the  prolongation  of  each  of  the  arms 
of  the  cross,  the  after  image  of  this  arm  glides  all  the  time  on 
itself  (fig.  177).  We  then  observe  that  there  exists  only  one 
position  of  the  head  for  which  this  is  possible;  for  every  other 
position  of  the  head  the  after  image  of  the  cross  turns  around 
during  the  displacement  of  the  look.  When  we  have  found  this 
position  of  the  head,  we  fix  the  planchette,  so  as  to  be  able  to 


THE  LAW  OF  LISTING 


351 


again  find  the  position  every  time  that  we  take  the  planchette 
between  the  teeth.  Then,  when  we  fix  the  point  A,  the  eye 
is  in  the  primary  position.  Suppose,  indeed,  that  we  fix  a  second 


X 


•x- -:> 


x 


X 


: x» 


x 


Fig.  178. 


point  B,  situated  on  a  prolongation  of  the  horizontal  arm  :  since 
the  meridian  which  was  horizontal  when  fixing  A,  is  also  hori- 
zontal when  fixing  B,  it  is  clear  that  the  look  may  be  brought 
from  A  to  B  by  a  motion  around  a  vertical  axis,  that  is  to  say, 
around  an  axis  perpendicular  to  the  two  directions  of  the  visual 
line.  It  is  the  same  for  displacement  in  the  vertical  direction. 
In  order  to  demonstrate  that  this  is  also  the  case  for  the  oblique 
displacements,  we  tilt  the  cross  (fig.  178).  It  is  then  easy  to 
prove  that  the  after  image  of  one  of  the  arms  of  the  cross 
glides  all  the  time  on  its  prolongation,  when  the  look  follows 
this  prolongation,  and  that,  consequently,  the  eye  turns  around 
an  axis  perpendicular  to  this  meridian.  The  law  of  Listing  is 
thus  verified. 

If,  in  these  experiments,  the  look  does  not  follow  the  pro- 
longation of  one  of  the  arms  of  the  cross,  we  observe  phe- 
nomena which  might  seem  in  contradiction  with  the  law  of 
Listing.  Thus  fixing  the  point  C  (fig.  177)  we  observe  that 


352  PHYSIOLOGIC  OPTICS 

the  after  image  of  the  vertical  arm  of  the  cross  is  no  longer 
vertical;  it  has  undergone  a  rotation,  and  the  upper  extremity 
is  carried  to  the  right.  A  little  reflection  shows  that  this  is 
simply  a  consequence  of  the  law  of  Listing,  and  that  the  mer- 
idian which  was  vertical  when  fixing  A,  cannot  remain  vertical 
when  the  eye  turns  around  an  axis  perpendicular  to  the  dir 
AC.  Bonders,  who  first  described  this  phenomena,  attri 
it  to  a  rotary  movement  (Raddrehung)  of  the  eye,  that  i 


Fig.  179. 

say,  a  rotation  around  the  visual  line,  but  it  is  clear  that  such 
a  rotation  cannot  take  place  since  the  axis  of  Listing  is  per- 
pendicular to  the  visual  line. — The  horizontal  arm  of  the  cross 
seems  to  have  suffered  a  rotation  in  a  contrary  direction,  but 
this  is  merely  the  result  of  the  projection  of  the  after  image 
on  a  plane  which  is  not  perpendicular  to  the  visual  line,  (i)  If 
we  project  the  image  on  the  concave  surface  of  a  hollow  hemi- 


(1)  [How  much  these  after  images  ought  to  be  inclined  towards  the  horizontal 
and  vertical  lines  of  the  wall  has  been  explained  by  the  translator  in  a  paper 
entitled  "The  Law  of  Listing  and  Some  Disputed  Points  about  Its  Proof,"  Archives 
of  Ophthalmology,  Vol.  XXVIII,  March,  1899.  The  relation  between  these  angles 
and  the  angles  of  Helmholtz  is  elucidated  in  a  paper  by  Dr.  G.  Hay  In  the 
Journal  of  the  Boston  Society  of  Medical  Sciences,  in  Oct.,  1899,  and  in  a  paper 
by  Professor  L.  Hermann,  in  Pflviger's  Archiv.  der  Physiologie,  Nov.,  1899.] — W. 


THE  LAW  OF  LISTING  353 

sphere,  in  the  center  of  which  is  the  eye,  the  cross  remains 
rectangular  and  seems  to  have  suffered  a  complete  rotation  to 
the  right  (fig.  179).— In  these  experiments,  the  position  of  the 
two  eyes  is  exactly  the  same:  we  can  cover  sometimes  one 
eye,  sometimes  the  other,  and  the  position  of  the  after  image 
does  not  change. 

must  be  noted  that  the  eye  may  be  transferred  from  the 
primary  position  to  a  secondary  position,  by  rotating  around 
the  axis  of  Listing.  I  do  not  say  that  it  really  makes  this  move- 
ment, for  the  law  of  Listing  defines  solely  the  position  of  the 
eye  in  the  state  of  repose. — We  know  nothing,  or  almost  nothing, 
of  the  manner  in  which  the  eye  makes  its  movements.  There 
is  no  reason  to  assert  that  it  turns  around  the  axes  of  Listing, 
nor  even  to  suppose  that  the  look  always  follows  the  same  way 
to  go  from  one  point  to  another.  The  best  method  of  studying 
this  question  would  probably  be  to  bring  the  look  quickly  from 
one  point  to  another,  leaving  the  eye  exposed  to  a  pretty  intense 
light.  The  after  image  of  the  luminous  -  source  then  assumes 
the  form  of  a  line  which  permits  some  conclusion  as  to  the 
nature  of  the  movement. 

What  we  have  said  suffices  to  determine  any  position  of  the 
eye.  If  the  look  passes  from  one  secondary  direction  to  another, 
the  position  of  the  eye  is  nevertheless  determined  by  the  law 
of  Listing,  since,  having  reached  its  new  secondary  position,  it 
must  have  the  same  position  as  if  it  had  reached  there,  starting 
from  the  primary  position.  Note  that  the  look  cannot  be  brought 
from  one  secondary  position  to  another  by  turning  around  an 
axis  perpendicular  to  the  two  directions  in  the  visual  line.  For, 
if  the  look  goes  from  B  to  C  (fig.  177),  following  the  prolonga- 
tions of  the  vertical  arm,  we  observe  that  the  after  image  of 
this  arm  starts  from  the  prolongation  and  rotates  more  and 
more  so  as  to  attain  the  position  which  it  should  have  when  the 
look  will  have  arrived  at  C.  In  making  this  movement  of  the 
look,  the  eye  does  not  rotate,  therefore,  around  an  axis  perpen- 
dicular to  the  visual  line,  and  we  can  in  this  case  speak  of  a 
true  rotary  movement.  If  we  displace  the  look  so  that  the  after 
image  moves  always  on  itself,  the  point  of  fixation  describes  a 


354  PHYSIOLOGIC  OPTICS 

curve  the  convexity  of  which  is  turned  towards  the  point  A.  It 
is  the  same  for  the  horizontal  arm:  if  we  bring  the  look  from 
C  to  E,  so  that  its  after  image  moves  on  itself,  we  obtain  a 
curve  with  its  convexity  downwards.  The  following  illusion, 
described  by  Helmholtz,  results  from  this  fact. 

If,  after  having  fixed  the  point  A  in  the  primary  position,  we  fc 
raise  the  eyes  and  survey  quickly  with  the  look  a  horizontal  * 
straight  line  situated  higher  up,  it  appears  concave  towards  the 
floor  (compare  page  261).  This  is  due  to  the  fact  that  oblique 
directions  of  the  look  are  very  rare.  Generally,  we  take  care 
when  we  desire  to  look  at  any  object,  to  turn  the  head  in  such 
a  way  that  the  eyes  are  nearly  in  their  primary  position,  and 
that  the  horizontal  lines  are  drawn  on  the  retinal  horizon  (the 
meridian  of  the  retina  which  is  horizontal  in  the  primary  posi- 
tion: in  the  experiment  fig.  177,  the  retinal  horizon  is  marked 
by  the  after  image  of  the  horizontal  arm  of  the  cross).  On  ac- 
count of  this  custom  we  have  a  tendency  to  consider  the  direc- 
tion of  the  retinal  horizon  as  horizontal,  even  when  it  is  not. 
Looking  upwards  and  to  the  left,  the  retinal  horizon  inclines 
its  right  extremity  downwards,  and,  if  we  consider  this  direc- 
tion as  horizontal,  it  follows  that  the  straight  line  which  we  ob- 
serve must  appear  inclined  to  the  left;  when  the  look  reaches 
the  other  extremity,  this  latter  will  seem  inclined  to  the  right; 
thus  it  is  that  the  line  assumes  its  curved  aspect,  but  we  must 
survey  it  quickly,  otherwise  it  seems  rather  to  lean  sometimes 
to  the  right,  sometimes  to  the  left. 

ANOTHER  METHOD  OF  DEMONSTRATING  THE  LAW  OF  LISTING. 
— As  the  retinal  horizon  passes  through  the  papilla,  we  can  use 
the  position  of  the  spot  of  Mariotte  to  account  for  its  direction. 
Pick  drew,  on  a  cardboard  movable  around  a  point  O,  a  black 
spot  just  large  enough  to  disappear  in  the  spot  of  Mariotte,  when 
he  fixed  the  point  O  in  the  primary  position.  Turning  the  head 
to  the  right  or  to  the  left  and  inclining  it  at  the  same  time,  while 
he  continued  to  fix  the  point  O,  the  spot  reappeared  and  he  then 
measured  how  much  it  was  necessary  to  turn  the  cardboard  to 
make  it  disappear  again. — Proceeding  thus,  we  find,  as  by  the 


THE  LAW  OF  LISTING  355 

preceding  method,  that  the  eyes  follow  pretty  exactly  the  law 
of  Listing,  at  least  while  the  visual  lines  remain  parallel. 

118.  Experiments  of  Meissner.— Apparently  vertical  meridian. 
— There  exists  another  method  which  has  been  described  by 
Meissner,  and  which  enables  us  to  verify  the  law  of  Listing  in 
a  very  exact  manner.  But  before  explaining  this  method,  I 
must  mention  a  singular  phenomenon  which  we  meet  when  we 
wish  to  judge  whether  a  line  is  vertical  or  not. 

We  hold  a  plumb-line  in  front  of  a  wall  painted  uniformly 
and  we  fix  a  point  situated  a  little  in  front  of  this  line  ( i )  : 
we  then  see  the  latter  in  double  homonymous  images,  and  we 
would  expect  to  see  two  vertical  and  parallel  lines ;  but  the  two 
lines  seem  to  converge  upwards :  seen  with  the  right  eye,  the 
upper  extremity  of  the  line  seems  to  lean  to  the  left.  If  we 
fix  a  point  situated  behind  the  line,  the  images  are  crossed  and 
seem  to  converge  downwards.  A  vertical  line  seen  with  one 
eye  only  does  not,  therefore,  appear  vertical,  but  its  upper  ex- 
tremity seems  to  lean  to  the  left  or  to  the  right,  according  as  it 
is  the  right  eye  or  the  left  eye  which  looks  at  it. — Looking  at 
a  rectangular  cross,  one  of  the  arms  of  which  is  horizontal  and 
the  other  vertical,  the  two  angles,  the  upper  right  and  lower 
left,  will  appear,  for  the  right  eye,  larger  than  the  other  two, 
while  the  contrary  takes  place  for  the  left  eye. 

Since,  for  the  right  eye,  a  vertical  line  appears  to  lean  to  the 
left,  there  must  exist  a  line  leaning  to  the  right,  which  seems 
vertical.  We  can  determine  the  direction  of  this  line  by  ob- 
serving a  white  disc  movable  around  its  center  and  on  which 
we  draw  one  diameter.  Along  the  border  is  a  scale  graduated 
in  degrees,  the  zero  of  which  corresponds  to  the  vertical  line, 
and  which  must  be  placed  so  as  not  to  be  visible.  The  observer 
tries  to  turn  the  disc  so  as  to  place  the  diameter  vertically.  With 
the  right  eye  he  places  nearly  always  the  upper  extremity  some 
degrees  too  far  to  the  right,  with  the  left  eye  some  degrees  too 


(1)  We  must  not  place  ourselves  too  near  the  line,  in  order  that  the  influence 
of  convergence,  of  which  I  shall  speak  immediately,  may  not  interfere. 


356  PHYSIOLOGIC  OPTICS 

far  to  the  left.  For  the  horizontal  meridian,  the  phenomenon  is 
less  pronounced. — It  is  necessary  to  arrange  the  experiment  in 
such  a  manner  that  the  observer  cannot  be  guided  by  the  view 
of  the  surrounding  objects. 

Another  method  of  determining  the  angle  between  the  ap- 
parently vertical  meridians  of  the  two  eyes  has  been  described 
by  Volkmann  (fig.  180).  He  placed  two  small  revolving  discs 
on  a  vertical  wall  so  that  the  distance  separating  their  centers 
would  be  equal  to  the  distance  between  the  eyes.  On  each  disc 
was  shown  one  radius.  He  observed  the  discs  as  with  the 
stereoscope,  the  right  eye  fixing  the  disc  on  the  right,  the 


Fig.  180. — Discs  of  Volkmann. 

left  eye  that  on  the  left.  He  placed  one  of  the  radii  vertically, 
and  then  tried  to  place  the  other  so  that  the  two  radii  would 
appear  to  form  a  single  straight  line ;  it  was  necessary  that  they 
should  form  an  angle  of  about  two  degrees. — Among  the  stereo- 
scopic tests  which  are  given  in  Jarval's  manual  on  strabismus, 
several  show  small  discs  like  those  of  Volkmann,  on  which  the 
two  radii  are  exactly  parallel.  On  overlapping  the  two  discs 
they  form  only  one,  but  the  diameter  appears  broken;  the  two 
radii  seem  to  form  an  obtuse  angle.  If  we  present  to  the  right 
eye  the  figure  which  was  intended  for  the  left  eye,  the  angle 
seems  turned  in  the  opposite  direction. 

It  is  probable  that  these  phenomena  are  due  to  the  more  im- 
portant part  played  by  the  downward  look  in  everyday  life:  we 
look  downwards  when  reading,  and  when  walking  the  look 
most  frequently  follows  the  ground,  etc.  By  repeating  the  ex- 
periment of  Meissner,  we  will  find  that  the  two  images  appear 


THE  LAW  OF  LISTING 


357 


parallel  if  we  bring  the  lower  extremity  of  the  plumb-line  to- 
wards the  observer,  until,  in  relation  to  the  line  of  the  look, 
it  has  almost  the  inclination  which  a  book  has  when  we  hold  it 
in  the  ordinary  position  of  reading.  If  we  draw  a  straight  line 
on  a  sheet  of  paper  placed  on  a  table  so  that  this  line  is  in 
the  median  plane  of  the  observer,  we  see,  on  placing  ourselves 
in  the  position  which  we  ordinarily  assume  in  order  to  read  or 
write,  making  the  visual  lines  parallel,  that  the  two  images  of 
the  line  appear  parallel.  Glancing  at  figure  181,  in  which  the 
eyes  are  shown  projected  on  the  table,  it  is  easy  to  see  that  the 
extremity  A  of  the  line  which  is  nearest 
the  observer  forms  its  image  on  more 
peripheral  parts  of  the  retina  than  the 
extremity  B.  The  two  meridians  of  the 
retinae  which  receive  the  images,  con- 
verge therefore  downwards,  since  the  ex- 
tremity A  forms  its  image  higher  and 
more  towards  the  periphery  than  the  ex- 
tremity B.  We  have  formed  our  judg- 
ment according  to  this  experiment,  and 
when,  under  other  circumstances,  a  line 
comes  to  form  its  image  upon  this  mer- 
idian, we  consider  it  as  situated  in  the 
median  plane.  According  to  Javal,  the 
experiments  establishing  binocular  vision 
in  persons  affected  with  strabismus,  con- 
firm absolutely  the  preceding  explanations. 

One  can  understand  how  these  methods  may  be  used,  if  not 
to  directly  verify  the  law  of  Listing,  at  least  to  compare  the 
position  of  the  two  eyes.  Working  in  the  primary  position,  and 
with  the  two  visual  lines  parallel,  Volkmann  found  that  it  was 
necessary  to  give  to  the  radii  of  his  discs  directions  converging 
about  two  degrees  downwards,  in  order  that  they  would  appear 
to  form  an  unbroken  line.  Leaving  the  visual  lines  parallel,  he 
found  the  same  angle  for  all  secondary  directions,  and  the  law 
of  Listing  was  thus  verified.  It  is  otherwise  when  we  converge. 
After  having  placed  the  eyes  in  the  primary  position,  Volkmann 


/A\ 


Fig.  181. 


358  PHYSIOLOGIC  OPTICS 

converged  for  a  point  situated  at  30  cm.  in  the  same  horizontal 
plane.  Since,  under  these  circumstances,  the  eyes  pass  from 
the  primary  position  to  an  internal  position,  the  law  of  Listing 
would  have  demanded  that  the  directions  of  the  two  radii  would 
continue  to  form  an  angle  of  two  degrees ;  but  Volkmann  found 
that  it  was  necessary  to  increase  their  inclination  to  four  de- 
grees, in  order  that  the  resulting  line  would  be  seen  unbroken. 
Converging,  each  eye  had,  therefore,  made  a  rotary  movement 
of  one  degree,  which  it  would  not  have  made  by  taking  the 
same  position,  if  the  visual  lines  were  parallel.  The  eyes  do 
not,  therefore,  follow  exactly  the  law  of  Listing  when  the  visual 
lines  are  not  parallel. 

The  following  experiment  is  very  easy  to  perform.  We  place 
two  candles  one  meter  from  each  other,  and  we  observe  them 
at  one  or  two  meters  distance,  taking  care  to  put  the  eye  nearly 
in  the  primary  position.  We  then  try  to  converge  as  if  to  fuse 
the  two  candles.  We  will  then  observe  that  they  appear  slightly 
inclined  towards  each  other;  the  nearer  to  each  other  we  bring 
the  candles,  the  greater  the  inclination;  the  angle  between  the 
two  candles  may  reach  15°  or  more.  The  image  of  the  left  eye 
is  inclined,  the  upper  extremity  to  the  right  and  vice  versa. 
Her'mg,  and  later  Landott,  have  made  exact  measurements  of 
these  deviations  from  the  law  of  Listing. 

119.  Historical. —  The  question  of  knowing  whether  the  eye 
performs  rotary  movements  around  the  visual  line  has  been 
much  disputed.  Hueck  thought  that  he  observed  that  the  eye 
undergoes  a  rotation  in  a  reverse  direction  when  the  head  is 
leant  towards  the  shoulder  so  that  the  meridian  of  the  retina, 
which  is  vertical  in  the  ordinary  circumstances  of  life,  remains 
vertical.  He  attributed  this  rotation  to  the  contraction  of  the 
oblique  muscles,  and  his  ideas  were  shared  by  all  scientists  until 
Ruete  demonstrated  the  error  of  Hueck  by  means  of  the  ex- 
amination with  the  after  images,  and  gave  a  correct  explana- 
tion of  the  action  of  the  oblique  muscles.  Bonders  took  up 
the  question,  and  enunciated  a  law  which  bears  his  name, 
according  to  which  the  position  of  the  after  image  is  always 


THE  LAW  OF  LISTING  359 

the  same  for  the  same  direction  of  the  eye;  but  the  question 
was  stated  clearly  only  by  the  enunciation  of  the  law  of  Listing, 
which  is  found  for  the  first  time  in  the  treatise  of  Ruete  of 
1853.  Listing  did  not  publish  it  himself.  Meissner  was  the  first 
who  verified  this  law  by  experiments. 

After  the  experiments  of  Ruete  and  Bonders  everybody  sup- 
posed the  rotary  movements  of  Hideck  did  not  exist,  when  Javal 
demonstrated  that  the  eye  performs,  nevertheless,  a  very  slight 
rotation  in  this  direction.  He  had  observed,  indeed,  that  when 
he  leant  his  head  to  the  right  or  to  the  left  the  direction  of 
the  axis  of  his  cylindrical  glasses  no  longer  coincided  with  that 
of  his  astigmatism.  This  is,  perhaps,  the  most  exact  test  to  see 
whether  glasses  are  properly  placed.  Helmholtz  verified  the 
fact  by  placing  on  a  level  with  his  eyes  a  small  colored  band 
on  a  frame  fixed  on  his  planchette.  By  leaning  the  head  with 
the  planchette,  the  secondary  image  turned  a  little  in  the  op- 
posite direction,  so  as  no  longer  to  coincide  with  the  ribbon. 

Bibliography. — CEuvres  de  Young,  edited  by  Tseherning,  p.  145. — Hueck. 
Die  Achsendrehung  des  Auges.  Borpat,  1838. — Bonders  (F.  C.).  Hol- 
Idndische  Beitrdge,  1848. — Ruete.  Lehrbuch  der  Ophthalmalogie,  1853. — 
Fick  (A.).  Die  Bewegungen  des  menschlichen  Augapfels.  Zeitschrift  fur 
rat.  Medizin,  IV,  1854. — Meissner  (G.).  Die  Bewegungen  des  Auges.  Arch, 
f.  Ophth.,  II,  1,  1855. — v.  Helmholtz.  Ueber  die  normalen  Bewegungen  des 
menschlichen  Auges.  Arch.  f.  Ophth.,  IX,  2,  1863. — Volkmann  (A.  W.). 
Physiologische  Unersuchungen  im  Gebiete  der  OptiJc.  II.  Leipzig,  1864. — 
Donders  and  Doyer  in  Bonders.  Anomalies  of  Refraction  of  the  Eye.  Lon- 
don, 1864,  p.  180. — Javal  (E.)  in  de  Wecker.  Traite  des  maladies  des 
yeux.  I,  p.  815.  Paris,  1866. — Tseherning  (M.).  La  loi  de  Listing. 
Paris,  1887. 


CHAPTER  XX 

THE  OCULAR  MOVEMENTS 

120.  Jerking  Movements  of  the  Eyes.— It  seems  as  if  the  eye 
should  be  kept  motionless  in  order  to  obtain  an  impression,  at 
least  an  impression  which  can  be  perceived  with  some  distinct- 
ness.    If,  in  a  railroad  train  which  is  going  quite  fast,  we  fix 
a  point  on  the  window,  the  landscape  appears  confused,  the 
images  of  its  different  parts  succeeding  one  another  too  quickly 
on  the  retinae  to  be  perceived  distinctly.    Observing  the  eyes  of 
any  one  who  is  looking  at  the  landscape,  we  see  that  they  move 
by  jerks.    The  eyes  of  the  person  observed  make  alternately  a 
rapid  movement  in  the  direction  of  the  train  to  catch  the  object, 
and  a  slower  movement  in  the  opposite  direction  to  keep  the 
image  of  the  object  on  the  fovea.     Then  they  again  make  a 
rapid  movement  with  the  train  to  catch  a  new  object,  and  so 
forth. 

The  eye  cannot  fix  the  same, point  for  even  a  little  while, 
without  the  formation  of  after  images  which  annoy  the  vision, 
and  without  the  phenomenon  of  Troxler  interfering.  The  eyes 
are,  therefore,  in  perpetual  motion  which  is  made  by  jerks: 
they  fix  a  point,  make  a  movement,  fix  another  point,  and  so 
forth.  While  reading,  the  eyes  move  also  by  jerks,  four  or 
five  for  each  line  of  an  ordinary  book.  Lamare  constructed  a 
small  instrument,  formed  by  a  point  which  is  supported  on  the 
eye  across  the  upper  eyelid,  and  which  is  fastened  to  the  ears 
of  the  observer  by  rubber  tubes.  With  this  instrument  each 
movement  of  the  eye  causes  a  sound  to  be  heard.  We  hear 
four  or  five  slight  sounds  during  the  reading  of  one  line,  and 
a  louder  sound  when  we  begin  to  read  a  new  line. 

121.  Relative  Movements  of  the  two  Eyes. — The  relative  move- 
ments of  the  two  eyes  are  governed  by  the  necessity  of  seeing 
the  object  single.    It  is  necessary  for  this  purpose  that  an  image 

360 


THE  OCULAR  MOVEMENTS  361 

of  the  object  fixed  be  formed  on  each  fovea.  When,  after  hav- 
ing looked  at  an  object  at  a  certain  distance,  we  look  at  another 
situated  at  the  same  distance,  the  two  eyes  make  associated  move- 
ments :  both  turn  to  the  right,  or  both  to  the  left,  upwards  or 
downwards,  etc.,  and  one  as  much  as  the  other.  If  the  objects 
are  both  in  the  median  plane,  but  at  different  distances,  it  is 
necessary,  in  order  to  bring  the  look  from  the  more  distant 
to  the  nearer,  that  the  eyes  make  a  movement  of  convergence: 
both  turn  inwards  to  the  same  extent;  finally,  if  the  two  objects 
are  in  different  directions,  the  second  nearer  than  the  first,  the 
eyes  perform  a  combination  of  an  associated  movement  and  a 
movement  of  convergence. — If  the  second  object  is  situated 
farther  away  than  the  first,  the  eyes  make  a  movement  of 
divergence  (negative  convergence). 

It  is  impossible  to  cause  a  movement  to  be  made  with  one 
eye  without  the  other  moving  also,  or  at  least  without  its  having 
a  tendency  to  move.  A]  very  simple  experiment  would  seem  to 
indicate  the  contrary.  Suppose  that  the  two  eyes  fix  a  point  a, 
and  that  we  place  in  the  visual  line  of  the  right  eye  an  object  b. 
If  we  ask  the  observed  person  to  fix  b,  the  left  eye  is  directed 
towards  this  point,  while  the  right  eye  remains  motionless.  But, 
if  we  observe  closely,  we  shall  see  that  this  eye  makes  really 
two  slight  changes  of  position,  for  instead  of  receiving  no  in- 
nervation,  as  one  would  think,  its  muscles  receive  two,  one  which 
would  cause  it  to  make  an  associated  movement  (to  the  right), 
and  another  which  would  cause  it  to  make  a  movement  of  con- 
vergence (to  the  left)  ;  the  results  of  these  two  innervations 
neutralize  so  that  the  eye  remains  motionless.  It  was  Hering 
who  described  this  experiment,  which  is  of  great  importance  for 
the  understanding  of  the  relation  between  the  movements  of 
the  two  eyes. 

The  two  kinds  of  movements  of  which  we  have  spoken  are 
the  only  ones  which  the  eyes  have  usually  to  make  in  the  in- 
terest of  fusion,  and  they  are  the  only  ones  which  they  can  make. 
It  is  possible,  however,  to  make  them  diverge  a  little. — I  mean 
absolute  divergence  and  not  relative  divergence,  which  is  only 


362  PHYSIOLOGIC  OPTICS 

a  less  degree  of  convergence. — We  can  make  this  divergence 
necessary  for  fusion  by  placing  before  one  eye  a  prism  with  its 
apex  turned  outwards;  but  the  angle  of  the  prism  which  the 
eyes  can  thus  overcome  does  not  much  exceed  fixed  degrees.  We 
are  unable  to  raise  the  look  of  one  eye  while  leaving  the  other 
motionless;  but  by  placing  before  one  eye  a  very  weak  prism, 
apex  upwards,  this  eye  deviates  a  little,  however,  in  the  interest 
of  fusion.  The  prism  which  we  may  thus  overcome  generally 
does  not  exceed  two  or  three  degrees. 

These  peculiarities  of  the  ocular  movements  are  evidently  not 
due  to  the  muscular  apparatus.  There  is,  indeed,  nothing  to 
prevent  the  right  eye  from  making  a  movement  to  the  right,  but 
it  cannot  make  it  while  the  left  eye  makes  a  movement  to  the 
left.  If  we  cannot  perform  two  movements  at  once,  this  is 
due  to  the  fact  that  we  cannot  give  the  necessary  innervation 
for  this  movement.  And  we  cannot  give  this  innervation  be- 
cause we  are  not  accustomed  to  give  it,  since,  far  from  being 
useful,  it  would  be  harmful,  on  account  of  the  diplopia  to  which 
it  would  necessarily  give  rise. — The  impulse  which  guides  the 
ocular  movements  is,  up  to  a  certain  point,  analogous  to  that 
which  makes  us  keep  our  eyes  open  and  the  head  erect,  with 
this  difference,  however,  that  the  innervation  which  guides  the 
movement  of  the  eyes  is  much  more  rigorous;  we  can  lower  the 
head  or  close  the  eyes  if  we  desire  to  do  so,  but  we  cannot  put 
the  eyes  in  divergence.  The  innervation  in  question  disappears 
during  sleep.  When  struggling  against  sleep,  we  observe  di- 
plopia, and  the  two  images  affect  relative  positions  which  they 
never  have  in  a  state  of  wakefulness.  The  homonymous  images 
whch  we  obtain  by  squinting  voluntarily  are  always  parallel,  if 
I  except  the  phenomena  mentioned  in  the  preceding  chapter, 
and  they  are  at  the  same  height  (if  the  head  be  kept  erect).  The 
images  which  we  obtain  when  sleep  conies  upon  us  have,  on 
the  contrary,  wholly  irregular  positions :  sometimes  one  is  higher 
than  the  other,  sometimes  they  undergo  rotations,  etc.  At  the 
same  time  the  eyelids  have  a  tendency  to  close  and  the  head 
to  fall. 


THE  OCULAR  MOVEMENTS  363 

122.  Measurement  of  Convergence. —  This  measurement  is  made 
preferably  with  the  rotary  prism  of  Cretes.  As  we  know,  this 
instrument  is  composed  of  two  superimposed  prisms  of  the  same 
strength.  A  special  mechanism  allows  them  to  be  turned  in 
opposite  directions.  When  the  apices  have  the  same  direction, 
the  effect  is  double  that  of  each  of  the  prisms.  If  we  cause 
them  to  rotate  the  deviation  always  takes  place  in  the  same 
direction,  but  it  gradually  diminishes  and  disappears  when  the 
apices  are  directed  in  different  directions.  The  instrument  re- 
places, therefore,  a  whole  series  of  prisms  of  different  strength. 

We  place  the  prism  with  the  apex  outwards  while  the  patient 
looks  at  a  distant  flame,  and  we  increase  the  strength  of  the 
prism  until  the  subject  sees  two  images  of  the  flame.  We  thus 
find  abduction;  for  healthy  eyes,  it  is  five  to  seven  degrees  of 
prism.  We  then  turn  the  prism  apex  inwards  and  increase  its 
strength  until  diplopia  is  produced.  Adduction  is  much  stronger 
than  abduction;  it  may  reach  20  or  30  degrees  of  prism,  or 
more.  We  can  also  measure  adduction  and  abduction  for  a 
nearer  point.  Adduction  often  exceeds  the  maximum  value  of 
the  prism  of  Cretes,  and  on  the  other  hand,  it  quite  frequently 
happens  that  it  is  greater  than  we  find  it  at  that  moment,  be- 
cause the  observed  person  does  not  do  his  best  to  fuse  the  images. 
It  would  also  be  better  to  measure  the  adduction  simply  by  try- 
ing how  near  we  could  approach  an  object  without  its  appearing 
double  (ophthalmodynamometer  of  Landolt). — We  sometimes 
meet  rare  cases  of  defect  of  convergence,  where  the  adduction 
is  greatly  diminished,  while  the  abduction  is  normal. — In  other 
cases  both  are  diminished :  the  patient  can  fuse  well  two  images 
which  are  formed  on  the  two  maculae,  but  he  experiences  no 
need  of  fusion;  even  when  the  double  images  are  very  near 
each  other,  the  eyes  do  not  make  the  slight  motion  necessary  to 
fuse  them. 

We  have  seen  (page  13)  that  the  deviation  produced  by  a 
prism  corresponds  nearly  to  half  its  angle.  If  we  can  overcome 
a  prism  of  six  degrees,  apex  outwards,  it  is  equivalent  to  saying 
that  we  can  make  the  visual  line  diverge  three  degrees.  This 
manner  of  indicating  the  degree  of  deviation  is  the  simplest,  and 


364 


PHYSIOLOGIC  OPTICS 


Fig.  182. 


that  which  is  most  frequently  used.  It  has  been  attempted  to 
introduce  another  notation  first  described  by  Javal,  and  after- 
wards adopted  by  Nagel.  This  author  names  meter  angle  the 
deviation  which  one  of  the  visual  lines  un- 
dergoes when,  after  having  fixed  a  point 
at  infinity,  we  look  at  a  point  situated  at 
one  meter  distance  on  the  visual  line  of  the 
other  eye.  o>  (fig.  182)  is,  therefore,  a 
meter  angle,  if  A  is  situated  at  a  distance 
of  one  meter;  two  meter  angles,  if  A  is 
at  50  centimeters,  and  so  forth.  The  sys- 
tem was  invented  to  measure  the  converg- 
ence in  a  manner  analogous  to  the  measure- 
ment in  dioptrics  which  we  use  for  refrac- 
tion (accommodation).  The  meter  angle 
corresponds  to  about  three  degrees  and  a 
half. — This  system  seems  to  offer  scarcely 
any  advantages,  and  it  has  this  quite  serious 
disadvantage,  that  the  value  of  a  meter 
angle  is  not  the  same  for  different  persons.  It  varies  with  the 
base  line. 

We  call  by  this  name  the  distance  between  the  centers  of 
rotation  of  the  two  eyes ;  it  varies  between  66  mm.  and  58  mm., 
or  still  less.  We  can  measure  it  by  sighting  a  distant  object,  a 
lightning  rod  for  example,  along  the  surface  of  a  planchette 
held  horizontally.  We  close  one  eye  and  fix  a  needle  in  the 
planchette,  so  that  it  may  appear  to  coincide  with  the  lightning 
rod.  The  needle  must  not  be  placed  too  near  the  eye  in  order 
that  its  images  may  not  be  too  diffuse.  Then  we  repeat  the 
experiment  with  the  other  eye  without  displacing  the  head; 
opening  the  two  eyes,  we  should  see  the  two  needles  blended 
into  one,  which  coincides  with  the  lightning  rod.  The  distance 
between  the  needles  is  equal  to  the  base  line. — We  find  also 
very  great  variations,  especially  if  we  examine  children,  whose 
base  line  is  manifestly  very  short. 

Now  it  is  clear  that  the  deviation  which  the  eye  must  undergo, 
in  order  to  pass  from  infinity  to  one  meter  distance,  is  so  much 


TEE  OCULAR  MOVEMENTS  365 

more  considerable  in  proportion  as  the  base  line  is  greater. — A 
meter  angle  corresponds  to  3°4(/  for  a  person  who  has  a  base 
line  of  64  mm.,  to  3°2(y  if  the  base  line  is  58  mm.  To  do  well, 
therefore,  it  would  be  necessary  each  time  we  measure  the  con- 
vergence in  meter  angles,  to  tell  also  the  length  of  the  base  line. 

Prentice  proposed  to  number  prisms  according  to  the  linear 
deviation  which  they  produce  at  a  given  distance,  observing  that 
at  a  distance  of  one  meter  the  deviation  produced  by  a  prism  of 
one  degree  is  about  one  centimeter. 

123.  Relations   between    Accommodation    and   Convergence. — 

In  the  interest  of  single  and  distinct  vision,  it  is  necessary  that 
there  be  formed  on  each  fovea  a  distinct  image  of  the  object 
fixed.  In  order  that  the  images  be  formed  on  the  two  foveas, 
it  is  necessary  that  the  individual  make  his  eyes  converge  to- 
wards the  observed  object,  and  in  order  that  the  images  be 
distinct,  it  is  necessary  that  each  accommodate  exactly  for  the 
object.  There  is  thus  formed  a  relation  between  accommodation 
and  convergence,  so  that  we  cannot  easily  converge  towards  an 
object  without  also  accommodating  for  this  object.  The  rule, 
however,  is  not  absolute;  we  can,  if  it  is  necessary  for  distinct- 
ness of  vision,  change  within  certain  limits  the  degree  of  accom- 
modation without  changing  the  degree  of  convergence.  This 
play  of  the  accommodation,  which  is  possible  while  the  converg- 
ence remains  the  same,  has  the  name  relative  amplitude  of  ac- 
commodation (Bonders).  We  can  measure  this  amplitude  by 
placing  convex  and  concave  glasses  before  the  eyes  until  the 
object  appears  double  or  diffuse. 

Bibliography. — Javal  (E.).  In  de  Wecker.  Traite  des  maladies  des 
yeux.  Paris,  1866. — Bonders.  Anomalies  of  the  Refraction  of  the  Eye. 
London,  1864. — Nagel  (A.).  Ueber  die  Beziehungen  dioptrischer  Werthe 
und  der  Betrdge  symmetrischer  Convergenzbewegungen  nach  metrischen 
Einheiten.  Mittheilungen  aus  der  ophtalmiatrischen  KliniTc  in  Tubingen. 
Tubingen,  1880.  Lamare.  Les  mouvements  des  yeux  dans  la  lecture.  Bull, 
de  la  Soc.  fr.  d'opht.  1882,  p.  354. — Prentice  (Ch.  F.).  Ein  metrisches 
System  zur  Bezeichnung  u.  Bestimtrwng  v.  Prismen.  Archiv.  f.  Augenheilk. 
XXII,  p.  215. 


CHAPTER  XXI 
THE  PROJECTION  OF  VISUAL  IMPRESSIONS 

124.  Projection  Outwards  in  TTniocular  Vision. — In  order  to  be 
able  to  form  a  correct  idea  of  the  position  of  an  exterior  ob- 
ject, it  is  necessary  to  be  informed  as  to  the  direction  and  dis- 
tance of  this  object.     Judgment  of  the  direction  is  formed  as 
well,  or  better,  with  a  single  eye;  the  superiority  of  binocular 
vision  is  apparent  in  the  judgment  of  distance,  but  at  the  same 
time,  in  the  matter  of  direction,  it  causes  certain  illusions  from 
which  persons  blind  of  one  eye  are  exempt.     We  shall  first 
discuss  the  vision  of  these  latter. 

GENERAL  LAW  OF  PROJECTION. — An  impression  of  any  point 
of  the  retina  is  projected  outwards  into  the  visual  field,  follow- 
ing the  line  of  direction;  that  is  to  say,  following  a  straight  line 
passing  through  the  retinal  point  and  the  nodal  point  of  the 
eye.  We  have  seen  that  inversely,  an  exterior  point  for  which 
the  eye  is  focused  forms  its  image  at  the  point  of  intersection 
of  the  line  of  direction  with  the  retina.  As  long  as  there  is 
question  only  of  objects  seen  distinctly,  the  law  of  projection  is 
equivalent  to  saying  that  we  see  exterior  objects  in  the  direction 
in  which  they  really  are.  The  law  of  projection  does  not  apply 
merely  to  the  ordinary  phenomena  of  vision:  all  the  retinal  im- 
pressions, the  phosphenes,  after  images,  entoptic  phenomena, 
circles  of  diffusion,  etc.,  are  projected  according  to  this  law, 
which  is  entirely  general.  As  exceptions  we  can  cite  only  the 
deformities  of  objects  seen  indirectly,  which  seem  to  show  that 
the  law  is  not  followed  very  exactly  for  very  peripheral  parts 
of  the  retina,  and  perhaps  for  some  of  the  illusions  which  I 
shall  mention  later. 

125.  Projection  of  the  Visual  Field. —  The  law  which  we  have 
just  announced  regulates  the  manner  in  which  we  localize  ob- 
jects in  the  visual  field,  but  it  does  not  regulate  the  projection 
of  the  visual  field  in  its  entirety.     The  latter  depends  on  the 
manner  in  which  we  judge  tJie  position  of  the  eye,  or  rather  the 
direction  of  the  visual  line.    If  in  uniocular  vision,  we  judge  cor- 

366 


THE  PROJECTION  OF  VISUAL  IMPRESSIONS  367 

rectly  the  direction  of  the  visual  line,  the  entire  visual  field  is 
projected  in  a  correct  manner.  We  shall,  therefore,  proceed 
to  discuss  the  means  by  which  we  form  this  judgment. 

Supposing  that  we  fix  a  point  A,  and  that  we  desire  to  fix 
another  point  B.  As  long  as  we  fix  A<  B  is  seen  in  indirect 
vision,  and  the  distance  between  the  images  enables  us  to  judge 
of  the  degree  of  innervation  necessary  to  bring  the  look  towards 
B;  generally  this  judgment  is  quite  exact  so  that  we  bring  the 
look  towards  B  almost  without  hesitation.  From  innervation  re- 
sults the  contraction  of  the  muscles,  the  change  of  position  of 
the  eye  and  the  change  of  the  retinal  image  until  B  forms  its 
image  on  the  fovea. — One  might  think  that  the  sensation  of  the 
more  or  less  considerable  contraction  of  the  muscles,  the  gliding 
of  the  eye  between  the  lids,  etc.,  could  furnish  us  with  informa- 
tion on  the  direction  of  the  visual  line,  but  this  is  not  so;  we 
judge  this  direction  solely  by  the  degree  of  innervation  which 
we  have  used  to  bring  the  look  into  this  direction.  This  fact  is 
well  established  by  the  observation  of  patients  affected  with 
ocular  paralysis.  If,  for  example,  we  tell  a  patient  affected  with 
paralysis  of  the  right  external  rectus  to  close  his  left  eye  and 
look  to  the  right,  he  furnishes  the  innervation  necessary;  the 
eye  remains  motionless  on  account  of  the  paralysis,  but  the  pa- 
tient thinks  he  has  moved  it  to  the  right,  so  that  there  results 
a  false  projection ;  if  we  tell  the  patient  to  move  his  finger  rapidly 
towards  an  object  situated  to  the  right,  not  having  time  to  guide 
himself  by  the  sight  of  the  finger,  he  constantly  moves  it  too  far 
to  the  right.  A  healthy  person  can  make  the  experiment  by 
looking  to  one  side,  while  he  exerts  a  traction  in  the  opposite 
direction  on  a  fold  of  the  skin,  near  the  external  canthus.  The 
traction  is  communicated  by  the  conjunctiva  to  the  globe,  and 
on  account  of  the  resistance  which  it  exerts,  one  is  obliged  to 
use  a  stronger  innervation  to  bring  the  look  to  the  opposite  side ; 
we  conclude  from  this  that  the  look  is  carried  farther  in  this 
direction  than  it  really  is,  which  causes  projection  of  the  visual 
field  in  a  false  manner. 

Judgment  of  the  degree  of  innervation  used  is  very  exact, 
because  it  is  always  corrected  by  the  result  obtained,  as  the  fol- 


368  PHYSIOLOGIC  OPTICS 

lowing  experiment  shows.  One  looks  directly  in  front  after  hav- 
ing put  a  prism  of  ten  degrees,  apex  to  the  left,  before  each 
eye.  Seen  through  the  prisms,  an  object  situated  at  ten  de- 
grees to  the  right,  appears  five  degrees  from  the  visual  line,  and 
we  need  only  an  innervation  corresponding  to  five  degrees  to 
fix  it;  we  think,  therefore,  that  it  is  situated  at  five  degrees  to 
the  right,  and,  if  we  wish  to  grasp  it,  we  do  not  bring  the  hand 
far  enough  to  the  right.  But  it  suffices  to  repeat  the  experi- 
ment only  a  few  times  in  order  to  be  no  longer  deceived:  we 
learn  very  quickly  to  reckon  with  prisms.  If  then  we  repeat 
the  experiment  after  having  removed  them,  we  bring  the  hand 
too  far  to  the  right. 

When  we  judge  correctly  the  direction  of  the  visual  line  there 
is  in  monocular  vision  no  possible  illusion  as  to  the  direction 
in  which  objects  are.  In  mathematics  we  often  determine  the 
position  of  a  point  by  means  of  what  are  called  polar  coordi- 
nates. Being  given  a  fixed  point,  named  center  of  coordinates, 
the  position  of  any  other  point  is  determined  by  the  direction 
and  length  of  the  radius  vector,  that  is  to  say,  of  the  line  which 
joins  the  two  points.  In  uniocular  vision,  the  center  of  co- 
ordinates is  represented  by  the  eye,  or,  more  exactly,  by  its 
nodal  point;  the  law  of  projection  gives  the  direction  of  the 
radius  vector.  To  know  the  exact  position  of  the  exterior  point, 
there  is  wanting,  therefore,  only  the  length  of  the  radius  vector, 
but  this  the  eye  does  not  give,  at  least  not  in  a  direct  manner. 

It  is  easy,  indeed,  to  convince  oneself  that  while  the  eye  in- 
forms us  very  exactly  on  the  direction  in  which  the  light  comes, 
it  gives  us  no  information  as  to  the  distance  whence  it  conies. 
The  information  which  the  greater  or  less  degree  of  accom- 
modation used  could  furnish  is  too  indefinite. — In  the  tenth 
chapter  I  laid  stress  on  the  importance  which  the  study  of  the 
form  under  which  a  distant  luminous  point  is  seen  may  have 
in  the  matter  of  exact  knowledge  on  the  optics  of  the  eye.  One 
might  think  that  one  can  replace  the  distant  luminous  point  by 
a  near  luminous  point  placed  at  the  focus  of  a  strong  lens.  If 
the  eye  would  inform  us  on  the  distance  whence  the  light  comes 
to  it,  the  result  of  the  two  experiments  ought  to  be  the  same, 


THE  PEOJECTION  OF  VISUAL  IMPRESSIONS  369 

since  the  rays  reaching  the  eye  are  parallel  in  both  cases.  But 
this  is  not  so.  Other  information  tells  us,  in  fact,  that,  in  the 
latter  case,  the  luminous  point  is  very  near,  which  makes  us 
see  the  figure  of  diffusion  extremely  small,  and  makes  this 
form  of  experiment  not  to  be  recommended.— We  know  also 
that  the  after  images  appear  to  us  large  or  small,  according  as 
we  project  them  on  a  distant  or  near  surface,  which  shows 
clearly  that  the  eye  does  not  accord  to  them  a  real  distance.  If 
we  do  not  present  to  them  a  surface  on  which  they  can  be  pro- 
jected, for  example  by  closing  the  eyes,  they  generally  seem  to 
have  the  same  apparent  size  as  the  object  of  which  they  are 
the  image;  we  accord  to  them  the  distance  of  this  object,  a 
distance  which  is  not  told  by  a  direct  sensation,  but  which  we 
judge  by  an  unconscious  reasoning,  as  we  shall  see  in  the  follow- 
ing chapter. 

126.  Projection  in  Binocular  Vision. —  The  impressions  of  the 
twc  macula  are  projected  towards  the  same  place.  When  the 
eyes  perform  their  functions  correctly,  both  of  them  always  fix 
the  same  object,  so  that  under  these  circumstances  the  fact 
stated  is  not  surprising.  But  it  is  the  same  when  they  do  not 
fix  the  same  object,  as  is  evident  among  others  from  stereoscopic 
experiments.  The  following  experiment  seems  to  me  to  demon- 
strate this  fact  in  a  very  striking  manner,  but  it  is  necessary 
to  be  able  to  squint  in  order  to  repeat  it.  It  is  quite  easy  to 
learn  to  squint  inwards ;  in  order  to  squint  outwards  we  take 
hold  of  a  fold  of  the  skin  near  the  outer  canthus  of  one  eye, 
while  we  look  towards  the  opposite  side. — To  perform  the  ex- 
periment, we  close  one  eye  and  look  at  the  flame  with  the  other, 
so  as  to  produce  an  after  image.  We  then  open  the  closed  eye 
and  select  a  point  which  we  fix  with  this  eye  while  we  are  en- 
deavoring to  squint.  We  then  see  the  after  image  place  itself 
on  the  point  of  fixation,  although  the  visual  line  of  the  eye  to 
which  it  belongs  is  not  at  all  directed  towards  this  point.  We 
can  squint  more  or  less  considerably,  placing  the  visual  line  in 
divergence  or  in  convergence:  as  long  as  the  other  eye  fixes 
the  point  of  fixation,  the  after  image  is  located  there  also. 


370 


PHYSIOLOGIC  OPTICS 


PHYSIOLOGIC  BINOCULAR  DIPLOPIA. — Let  A,  figure  183,  be 
an  object  which  both  eyes  fix,  B  another  nearer  object.  If  we 
close  the  right  eye,  the  point  B  is  seen  five  degrees  to  the  right 
of  A;  if  we  close  the  left  eye,  it  is  seen  five  degrees  to  the  left 
of  A.  Opening  both  eyes,  A  is  seen  single  at  the  place  where  it 
really  is;  we  see  two  images  of  B,  one  five  degrees  to  the  left, 
the  other  five  degrees  to  the  right  of  A. — Wie  therefore  see  B 
in  double  crossed  images;  if  we  fix  B,  A  is  presented  in  double 
homonymous  images. — We  can  perform  the  experiment  with 
two  candles,  and,  if  necessary,  we  can  make  the  diplopia  more 
striking  by  placing  a  red  glass  in  front  of  one  eye. 

This  singular  phenomenon,  which  had  already  been  described 
by  Alhazen,  is  known  as  physiologic  binocular  diplopia. 

CENTER  OF  PROJECTIONS. — We  observe  that  the  correct  in- 
formation which  the  eyes  furnish  to  us  gives  rise  to  a  false 
interpretation,   for  it  is  evident  that,   when  an  object  is  seen 
double,  there  is  at  least  one  of  the  images  which  does  not  coin- 
cide with  the  object.     When 

Dl  •  •    •  ">]P        we  close  one  eye,  the  corre- 

sponding image  disappears, 
while  the  other  image  does 
not  change  position.  The 
false  judgment  must,  there- 
fore, persist  also  in  this  case, 
at  least  for  one  of  the  eyes. 
The  sight  of  normal  persons 
does  not,  therefore,  necessar- 
ily become  similar  to  that  of 
a  one-eyed  person. 

The  physiologic  diplopia  is 
due  to  the  fact  that  we  do  not 
take  into  consideration  the 
different  position  of  the  two 
eyes ;  without  a  special  exam- 
ination we  cannot  tell  whether 
an  image  belongs  to  one  eye 
or  the  other.  We  refer  every 


Fig.  183. 


THE  PROJECTION  OF  VISUAL  IMPRESSIONS  371 

visual  impression,  from  whatever  eye  it  may  come,  to  a  common 
and  single  center,  which,  in  my  case,  coincides  pretty  exactly 
with  the  right  eye.  Recalling  the  mathematical  terms  which  we 
have  used  in  the  preceding  chapter,  we  may  say  that  it  is  the 
center  of  the  co-ordinates  the  position  of  which  we  judge  im- 
perfectly. If  we  took  into  account  the  different  position  of  the 
two  eyes,  we  would  have  two  centers  of  co-ordinates,  and  the 
idea  of  the  direction  of  the  object  would  suffice  to  fully  deter- 
mine its  position.  In  the  experiment  (fig.  183)  we  would  thus 
reason  as  follows:  Since  we  see  with  the  right  eye  an  object 
five  degrees  to  the  left  of  A,  with  the  left  eye  the  same  ob- 
ject five  degrees  to  the  right  of  A,  the  object  must  be  in  the 
middle  plane  and  nearer  than  A;  we  would  therefore  see  B 
single  and  in  its  right  place.  Instead  of  this  we  refer  the  im- 
pressions, as  in  uniocular  vision,  to  a  single  center,  and  we 
inform  ourselves  that  the  object  must  be  double,  since  it  is  seen 
at  once  to  the  right  and  the  left. 

DIRECTING  EYE.  (i) — In  my  case  this  center  of  coordinates 
coincides  almost  exactly  with  the  right  eye,  probably  because, 
having  used  it  so  much  separately,  I  have  acquired  the  faculty 
of  judging  exactly  with  this  eye  the  position  of  exterior  ob- 
jects, or,  in  other  words,  because  there  is  developed  a  kind  of 
uniocular  vision  in  addition  to  binocular  vision.  I  must  add, 
however,  that  this  condition  was  not  developed  as  a  result  of 
my  labors  on  physiologic  optics,  because  the  phenomena  were 
the  same  when,  twelve  years  ago,  I  began  to  devote  my  atten- 
tion to  this  subject.  According  to  Hering  the  center  is  often 
at  an  equal  distance  between  the  two  eyes,  and  this  would,  in 
fact,  be  the  true  type  of  binocular  vision,  in  which  neither  of 
the  eyes  plays  a  dominant  part. — The  reasons  why  I  say  that 
in  my  case  the  center  of  projections  coincides  with  the  right 
eye,  are  as  follows: 


(1)  According  to  a  communication  from  Javal,  the  binocular  vision  of  Valtee 
was  like  mine.  He  described  this  condition  as  general  (in  a  communication  to 
the  Academy  of  Sciences,  about  1830),  and  gave  the  name  directing  eye  to  the 
eye  which  controls  projection  outwards.  H.  Kaiser  has  also  described  the  same 
condiiton  for  his  eyes. 


372  PHYSIOLOGIC  OPTICS 

i°  When  on  looking  at  a  distant  object  I  see  a  near  object 
in  double  crossed  images,  and  when  I  try  to  touch  this  object 
by  a  quick  motion,  I  grasp  it  correctly  if  I  sight  the  image  with 
the  right  eye,  while  I  bring  the  hand  far  from  the  object  if  I 
sight  the  image  with  the  left  eye.  It  is  the  same  if  I  close  one 
eye.  With  the  right  eye  I  judge  accurately  the  position  of  ob- 
jects seen  indirectly,  as  a  one-eyed  person  would  do;  with  the 
left  eye  I  judge  falsely.  Thus,  in  the  experiment  figure  183, 
closing  the  right  eye,  I  see  B  five  degrees  to  the  right  of  A,  as 
I  ought  to,  but  I  refer  the  impression  to  my  right  eye,  and, 
thinking  that  the  object  B  is  five  degrees  to  the  right  of  the 
visual  line  of  my  right  eye,  in  order  to  reach  it  I  bring  my  hand 
toward  Br — I  have  also  noticed,  especially  when  I  observe  the 
double  images  of  near  objects,  accidentally  and  without  trying 
to,  that  one  of  them,  that  of  the  right  eye,  presents  a  more 
material  appearance,  while  the  other  rather  resembles  a  kind 
of  shadow;  Dr.  Knapp,  Jr.,  made  the  same  remark  to  me.  It 
must  be  noted  that  my  eyes  are  practically  equal,  as  to  acuity 
and  refraction. 

2i°  I  fix  a  mark  P  (fig.  184),  not  too  bright,  placed  on  a 
dark  and  uniform  background.  Interposing  a  stick  between  my 
eyes  and  the  background,  on  the  visual  line  of  the  right  eye,  I 
see  it  in  double  images;  the  image  of  the  right  eye  (d)  coin- 
cides with  the  mark  of  fixation,  while  the  image  of  the  left 
eye  is  seen  more  to  the  right  (g)  (fig.  184  Ai).  If  now  I  fix 
the  stick,  it  is  the  image  g  of  the  left  eye  which  is  brought  to- 
wards that  of  the  right  eye,  d,  in  order  to  coincide  with  it,  while 
the  latter  remains  motionless.  One  might  think  that  this  is  due 
to  the  fact  that  I  placed  the  stick  on  the  visual  line  of  the  right 
eye,  but  this  is  not  so ;  if  I  place  the  stick  on  the  visual  line  of 
the  left  eye  (fig.  184,  B)  so  that  the  image  of  the  right  eye  d 
is  seen  to  the  left,  it  is  still  the  latter  which  remains  motionless, 
while  that  of  the  left  eye  makes  a  great  movement  to  join  itself 
to  it  when  I  fix  the  stick. — This  apparent  movement  exists  also 
when  I  close  the  right  eye,  although,  under  these  circumstances, 
the  left  eye  does  not  make  any  movement.  Under  this  latter 
form  the  experiment  was  described  by  Bering. 


THE  PROJECTION  OF  VISUAL  IMPRESSIONS  373 

3°  This  author  furthermore  described  the  following  experi- 
ment: we  fix  binocularly  an  object  placed  at  some  distance  in 
the  median  plane,  and  we  try,  by  a  quick  movement,  to  place  a 
stick  quite  near  the  face  in  the  direction  in  which  we  see  the 
object;  it  is  better  to  conceal  the  movement  of  the  hand  with  a 
screen.  Making  this  experiment,  I  bring  the  stick  pretty  exactly 
on  the  visual  line  of  the  right  eye.  The  experiment  is  easy  to 
repeat  even  with  persons  who  are  not  accustomed  to  study  such 


Fig.  184. 

questions,  and  we  can  control  by  placing  ourselves  in  front  of 
the  observed  person  and  sighting  with  one  eye  along  the  mark 
of  fixation  and  the  space  between  the  eye-brows  (glabclla)  of 
the  observed  person.  I  have  observed  several  persons  in  this 
way.  Most  of  them  show  a  marked  tendency  to  prefer  one 
or  other  eye,  which  seems  to  indicate  a  tendency  to  a  develop- 
ment of  a  uniocular  vision  in  addition  to  the  binocular  vision 
like  that  which  I  have  described  for  my  eyes.  Persons  en- 
joying pure  binocular  vision  must  place  the  stick  in  the  median 
plane;  as  the  center  of  projection  does  not  coincide  with  either 


374 


PHYSIOLOGIC  OPTICS 


of  the  eyes,  these  people  cannot  project  correctly  objects  seen 
indirectly.  This  type  of  vision,  therefore,  seems  inferior  to 
the  other,  as  far  as  orientation  is  concerned. 

HOROPTER. — All  the  points  outside  the  point  fixed  are  not  seen 
double;  the  point  C  (fig.  183),  for  example,  is  seen  ten  degrees 
to  the  right  of  A,  as  well  with  the  right  eye  as  with  the  left 


Fig.  185. — Horopter  of  Johannes  Muller. 

eye;  it  is  therefore  seen  single. — The  entirety  of  the  points  seen 
single  while  we  fix  a  given  point,  is  called  horopter. — The  study 
of  the  horopter  is  quite  a  complicated  mathematical  problem,  and 
without  much  interest,  since  the  diplopia  is  only  very  slightly 
indicated  when  the  object  is  a  little  distant  from  the  point  of 
fixation.  It  may  be  solved  when  we  know  the  position  of  the 
corresponding  points  (see  the  following  chapter)  and  the  law 
which  regulates  the  position  of  the  eyes  (law  of  Listing).  When 
the  point  of  fixation  is  in  the  plane  which  contains  the  primary 
position  of  the  visual  lines,  we  see  single  all  the  points  which  are 


THE  PROJECTION  OF  VISUAL  IMPRESSIONS  375 

on  a  circle  passing  through  the  point  of  fixation  and  the  nodal 
points  (horopter  of  Johannes  Mutter,  fig.  185).  It  is  easy  to 
see  that  on  fixing  A,  B  is  seen  single,  because  the  two  angles 
designated  by  a  are  equal,  since  both  correspond  to  the  arc  AB. 
— If  we  fix  a  point  on  the  floor,  situated  in  the  median  plane, 
the  horopter  corresponds  almost  to  the  plane  of  the  floor. 

SUPPRESSION  OF  DOUBLE  IMAGES. — As  one  sees  some  exterior 
objects  double,  and  some  single,  one  might  think  that  it  would 
result  in  great  confusion.  It  does  not:  most  people  have  never 
observed  double  physiologic  images  before  making  the  experi- 
ment described  above.  Under  ordinary  circumstances  the  at- 
tention is  always  brought  to  bear  on  the  object  fixed,  and  the 
look  never  remains  for  any  length  of  time  on  the  same  object, 
so  that  we  have  not  much  time  to  perceive  double  images.  It 
must  also  be  observed  that  the  objects,  not  fixed,  form  their 
images  on  the  peripheral  parts  of  the  retina,  where  the  percep- 
tion is  less  distinct  than  at  the  macula.  It  is  scarcely  possible 
to  suppose  a  serviceable  binocular  vision  if  the  entire  retina  had 
an  acuity  like  that  of  the  fovea.  But  we  also  make  important 
use  of  the  phenomenon  known  under  the  name  of  neutralization 
of  images,  and  which  has  been  given  special  prominence  by  the 
works  of  Javal  on  the  vision  of  persons  affected  with  strabismus 
(see  chapter  XXIII). 

In  addition  to  the  fact  that  most  of  the  time  an  object  seems 
to  be  at  two  different  places,  binocular  vision  gives  rise  to  yet 
another  contradiction.  Making  the  experiment  with  the  two 
candles  before  the  screen  DE  (fig.  183),  we  have  seen  that  the 
right  eye  sees  the  candle  B  at  five  degrees  to  the  left  of  A;  in 
this  direction  the  left  eye  sees  a  part  of  the  screen ;  and  as  we 
do  not  take  into  consideration  the  different  position  of  the  two 
eyes,  but  refer  our  impressions  to  a  common  center,  the  result 
is  that  we  seem  to  see  two  objects  in  the  same  direction.  Inter- 
posing a  stick  between  the  eyes  and  a  book  (controlled  reading 
of  Javal)  we  can  read  without  interruption  only  when  both  eyes 
are  open ;  if  we  close  one  eye,  the  stick  covers  some  of  the  char- 
acters. We  here  meet  the  same  contradiction;  we  see  the  stick 


376  PHYSIOLOGIC  OPTICS 

in  the  same  direction  as  the  characters  which  it  conceals,  and  as, 
on  the  other  hand,  we  know  that  it  is  nearer  than  the  book  it 
appears  transparent.  But,  in  cases  in  which  such  an  interpreta- 
tion is  not  possible,  for  example  when  we  present  to  both  eyes 
wholly  different  images,  in  a  stereoscope,  we  observe  what  is 
called  antagonism  of  the  visual  fields.  It  is  sometimes  the  im- 
ages of  one  eye  that  predominate,  sometimes  those  of  the  other, 
and  as  long  as  we  see  in  a  part  of  the  visual  field  images  of  one 
eye,  those  of  the  other  are  completely  suppressed. 

It  seems  that  this  suppression  of  the  images  of  one  eye  plays 
a  great  part  in  binocular  vision,  and  that  it  is  this  which  gener- 
ally causes  us  not  to  observe  double  physiologic  images. — It  is 
not  easy  to  know  which  of  the  two  images  is  suppressed,  for  as 
soon  as  we  pay  attention  to  this  question  both  appear.  Gen- 
erally it  is  the  more  eccentric  image,  or,  in  other  cases,  the 
image  which,  on  account  of  the  perspective,  occupies  the  smal- 
lest retinal  surface  (Javal)  which  disappears.  But,  in  most 
persons,  there  seems,  as  I  have  already  stated,  to  be  developed 
a  certain  superiority  of  the  eye  which  is  most  frequently  used 
separately,  and  then  it  is  always  the  image  of  the  other  eye 
which  is  suppressed. 

Bibliography. — Muller  (Johannes).  Beitrdge  zur  vergleichenden  Physi- 
ologic des  Gesichtssinnes.  Leipzig,  1826. — Hering  (E.).  Beitrdge  zur  Physi- 
ologic. Leipzig,  1861. — Kaiser  (H.).  Compendium  der  physiologischen 
Optik.  Wiesbaden,  1872,  p.  298. 


CHAPTER  XXII 
MONOCULAR  PERCEPTION  OF  DEPTH 

127.  Influence  of  Accommodation. —  I  have  already  said  that 
the  eye  gives  us  no  direct  information  as  to  the  distance  from 
which  light  comes  to  it.     We  might  think  that  the  degree  of 
accommodation  used  in  order  to  see  the  object  distinctly  would 
inform  us  as  to  its  distance.     When  the  eye  is  accommodated 
for  distant  objects,  near  objects  do  not  appear  distinct,  and  an 
experienced  observer  might  use  this  circumstance  to  judge  of 
the  distance  of  an  object.     Young  said  that  painters  must  take 
care  to  show  near  objects  vaguely  under  penalty  of  obtaining 
a  hard  and  disagreeable  effect.    But  the  importance  of  accommo- 
dation for  the  judgment  of  distances  is  but  small,  because,  gen- 
erally, we  are  dealing  with  such  long  distances  that  the  difference 
of  accommodation  is  insignificant.     For  all  distances  exceeding 
one  meter,  the  variation  of  accommodation  does  not  reach  one 
dioptry. 

128.  Indirect  Judgment  of  Distance. —  In  the  absence  of  direct 
information,  a  whole  series  of  circumstances  enable  us  to  judge 
of  the  distance  of  an  object,  generally  by  an  unconscious  judg- 
ment. 

a.  The  knowledge  of  the  nature  of  objects  often  furnishes  us 
with  a  means  of  knowing  their  distances.  Thus,  if  we  know 
the  size  of  an  object,  we  can  judge  its  distance  from  its  angular 
size.  It  is  the  size  of  man  especially  which  enables  us  to  make 
this  judgment.  Generally  we  judge  directly  of  distance.  When 
we  see  a  man  very  far  off,  he  does  not  appear  to  us  small,  be- 
cause we  know  what  size  he  ought  to  be,  but  we  conclude  that 
he  must  be  very  far  away,  since  the  angular  size  is  small,  and 
this,  without  this  latter  fact  directly  striking  our  consciousness. 
This  observation  is  quite  characteristic  of  the  manner  in  which 

377 


378  PHYSIOLOGIC  OPTICS 

unconscious  judgments  are  formed  and  it  must  be  noted  that 
this  way  of  judging  is  something  to  be  learned.  I  recall  very 
well  that  the  first  time  I  saw  a  man  climb  the  mast  of  a  ship, 
he  appeared  to  me  like  a  doll,  and  Helmholts  reports  a  similar 
observation. — If  we  look  at  distant  objects  through  a  telescope 
they  are  enlarged;  but  as  long  as  we  have  to  do  only  with  ob- 
jects of  known  size,  such  as  men,  houses,  etc.,  they  seem  to 
preserve  their  natural  size,  but  appear  near.  We  must  open 
the  other  eye  to  convince  ourselves  that  they  are  really  en- 
larged. 

b.  A  means  which  is  often  used  to  judge  whether  one  object 
is  nearer  than  another,  is  to  observe  whether  it  conceals  a  part 
of  the  other.    If  one  hill  conceals  the  lower  part  of  another  hill 
it  must  be  nearer. 

c.  If  we  are  acquainted  with  the  object  at  which  we  are  look- 
ing, or  if  there  is  a  certain  regularity,  we  easily  come  to  know 
what  part  is  nearest.    On  the  photograph  of  a  house,  we  easily 
judge  the  distance  at  which  the  different  parts  ought  to  be, 
while  photographs  of  rocks,  landscapes,  etc.,  are  frequently  more 
difficult  to  interpret. 

&  The  shadows  thrown  are  often  important  for  the  judgment 
of  distance.  If  a  surface  is  illuminated,  the  luminous  source* 
must  be  in  front  of  it,  and  if  an  object  casts  a  shadow  on  this 
surface,  it  must  be  nearer  the  observer  than  the  surface.  It  is 
for  this  reason  that  we  obtain  a  much  better  idea  of  the  reality 
by  adding  shading  to  a  drawing. 

e.  Finally,  aerial  perspective  sometimes  influences  the  idea 
which  we  form  of  distance.  We  comprise  under  this  term  the 
darkening  and  change  of  color  which  distant  objects  undergo  on 
account  of  the  incomplete  transparency  of  the  layers  of  air  which 
separate  them  from  the  observer.  The  vapors  of  water  which 
are  in  the  atmosphere  reflect  the  blue  rays,  and  allow  the  red 
rays  to  pass.  Comparing  the  spectra  of  a  blue  sky  and  a  cloudy 


MONOCULAR  PERCEPTION  OF  DEPTH  379 

sky,  Lord  Rayleigh  thus  found  that  the  brightness  of  the  latter 
diminishes  greatly  towards  the  blue  extremity.  When  the  spectra 
had  the  same  brightness  in  the  red,  the  green  of  the  cloudy  sky 
was  already  less  strong  than  that  of  the  blue  sky.  It  is  for  this 
reason  that  the  setting  sun  appears  red,  and  distant  mountains 
blue.  When  there  is  much  water  vapor  in  the  atmosphere,  we 
see  distant  objects,  such  as  forests  and  hills,  more  distant  and 
consequently  larger  than  they  really  are.  In  the  mountains  the 
air  is,  as  a  rule,  very  pure,  which  causes  us  to  often  judge  the 
distance  and  height  of  the  summits  much  smaller  than  they  really 
are. 

We  know  that  the  sun  and  moon  appear  larger  when  they 
are  near  the  horizon,  which  is  merely  an  illusion.  If  we  measure 
their  angular  size,  we  find  it  exactly  the  same  in  both  cases. 
Likewise,  if  we  try  to  divide  the  distance  between  the  zenith 
and  the  horizon  into  two  equal  parts,  we  are  greatly  deceived; 


Fig.  186.    After  Young. — The  curve  indicates  the  apparent  form  of  the  sky. 
The  sun,  although  seen  under  the  same  angle,  seems  of  variable  size. 

the  lower  part  is  always  too  small.  Since  the  moon,  near  the 
horizon,  appears  larger  than  near  the  zenith,  although  it  has  the 
same  angular  size,  it  is  equivalent  to  saying  that  we  judge  it  to 
be  farther  away.  The  illusion  is  due  to  the  aerial  perspective. 
The  moon  is  seen  through  a  much  thicker  layer  of  the  terrestial 
atmosphere  when  it  is  near  the  horizon  than  when  it  is  at  the 
zenith.  It  seems,  however,  that  the  comparison  with  terrestial 
objects  also  plays  a  part  in  this  judgment  (fig.  186). 

These  different  means  enable  us  to  judge  more  or  less  exactly 
of  the  distance  of  an  object.  They  are  especially  useful  to  us 
when  we  have  to  do  with  long  distances,  on  which  the  parallax, 
of  which  I  am  about  to  speak,  cannot  give  any  information. 


380  PHYSIOLOGIC  OPTICS 

129.  Influence  of  the  Parallax. —  The  idea  which  we  obtain 
of  the  relief,  by  displacements  of  the  head,  is  well  known  to  all 
who  use  the  ophthalmoscope.  We  thus  obtain  a  very  distinct 
idea  of  the  depth  of  an  excavation,  etc. — We  often  use  this 
means,  without  knowing  it,  to  study  an  object  difficult  to  inter- 
pret, and  it  is  the  principal  means  by  which  one-eyed  people  ac- 
count for  the  relief.  The  observer  often  sees  thus,  without  his 
perceiving  that  he  does  so,  the  relative  movements  of  exterior 
objects,  and  he  uses  them  to  account  for  their  position.  If,  for 
example,  while  the  eye  is  displaced  from  a  to  &  (fig.  187)  the 
observer  sees  the  object  A  displaced  to  the  right  relatively  to 
the  object  B,  A  must  be  nearer  than  B;  to  draw  this  conclusion, 
we  need  not  look  during  the  displacement.  If,  after  having 
observed  the  objects  in  the  position  a>  we  close  the  eye  to  open 
it  again  only  in  the  position  b,  we  observe,  nevertheless,  that  A 
has  changed  place  relatively  to  B,  which  suffices  to  judge  of  its 
distance. 

The  judgment  is  here  based  on  the  comparison  of  the  succes- 
sive retinal  images;  images  change  for  each  new  position  of  the 
x^          eye.    But,  as  all  comparison  by  memory 
is  defective,  we  obtain  a  much  more  dis- 
tinct idea  of  the  difference  between  the 
images,  and  consequently  of  the  relief, 
by  comparing  the  images  simultaneously 
AJf       r  with  the  two  eyes,  and  it  is  for  this  rea- 

son that  we  always  judge  distances  bet- 
ter with  two  eyes  than  with  one.  It  is 
easy  to  convince  ourselves  that  this  is 
so  by  trying  to  reach  a  stick  placed  at 
some  distance  with  the  finger  coming 
from  the  side.  Looking  with  one  eye 
__  ^.^  only  we  are  deceived  much  more  fre- 

(       ]  «4 (       j          quently  than  when  we  open  both  eyes. 

^-^  ^7  When  we  look  with  the  two  eyes,  each 

Fig.  187.  eve  recejves  a  perspective  image  of  the 

objects  situated  in  front  of  us;  as  the  two  eyes  are  not  at  the 

same  place,  there  result  between  the  images  differences  which 


MONOCULAR  PERCEPTION  OF  DEPTH  381 

are  the  more  pronounced  the  smaller  the  distance  of  the  object. 
If,  on  the  contrary,  we  look  at  a  plane  image  with  both  eyes, 
the  retinal  images  are  identical.  This,  therefore,  is  a  sign  by 
which  the  appearance  of  an  object  of  three  dimensions  is  dis- 
tinguished from  a  plane  image.  It  is  only  for  near  objects  that 
this  difference  exists:  if  the  objects  are  at  a  great  distance,  the 
retinal  images  are  alike;  thus  a  landscape  presents  almost  the 
same  appearance  whether  we  close  one  eye  or  whether  we  open 
both. 

Bibliography. — (Euvres  de  Young,  edited  by  Tscherning,  p.  244. 


CHAPTER  XXIII 
BINOCULAR  PERCEPTION  OF  DEPTH 

130.  Influence  of  Convergence. —  The  most  important  informa- 
tion on  the  distance  of  an  object  is  furnished  us  by  the  degree 
of  convergence  which  it  is  necessary  to  use  to  fix  it  binocularly. 
Just  as  for  the  judgment  of  the  direction  of  the  visual  line  in 
uniocular  vision  (see  ch.  XIXI),  it  is  the  degree  of  innervation 
used  which  guides  us,  and  not  at  all  the  sensation  of  the  position 
of  the  eyes,  which  is  always  very  vague.     It  is  solely  for  differ- 
ences of  convergence  that  we  have  a  very  exact  sensation;  we 
can   judge   with   very  great   exactness   whether   one   object   is 
nearer  or  farther  away  than  another;  the  judgment  of  absolute 
distance  is  very  uncertain. — When  we  fix  a  distant  object,  a 
near  object  appears  in  double  crossed  images.    Although  we  may 
not  often  perceive  these  images,  they  give  us,  nevertheless,  a 
vague  idea  of  the  distance^of  the  object,  for  they  suffice  to  give 
a  pretty  accurate  impulse  to  convergence,  since,  guided  by  them, 
we  converge  for  the  object  without  much  effort.    But  it  is  only 
after  having  accomplished  convergence  and   having  seen  that 
the  innervation  given  has  attained  its  object,  that  we  have  an 
accurate  idea  of  the  distance.    The  difference  between  the  two 
judgments  is  almost  analogous  to  that  which  we  find  when  we 
wish  to  measure  the  distance  between  two  points.    Suppose  that 
we  wish  to  measure  this  distance  with  a  compass,  provided  with 
a  scale  graduated  in  millimeters,  telling  the  distance  between 
the  two  points.    We  can  readily,  at  first  sight,  give  to  the  com- 
pass  approximately  the  aperture  which  is  necessary,   but   we 
obtain  a  more  exact  and  distinct  idea  of  the  distance  when  we 
make  the  measurement  and  see  how  much  must  be  added  to 
or  taken  away  from  the  estimated  distance. 

131.  The  Stereoscope. —  The  advantage  of  binocular  vision  was 
made  clear  only  by  the  invention  of  the  stereoscope  by  Wheat- 

382 


BINOCULAR  PERCEPTION  OF  DEPTH 


383 


stone  (1833).  With  this  instrument  we  obtain  an  impression 
of  depth  much  superior  to  that  which  any  other  representation 
can  give  of  it. 

Each  of  the  images  of  the  stereoscopic  representation  is  drawn 
in  such  a  way  as  to  form  in  the  eye  a  retinal  image  like  that 
which  the  object  would  form  there.  Distant  objects  are,  there- 
fore, represented  by  images  which  are  identical,  while  the  im- 
ages of  near  objects  are  different. 

STEREOSCOPIC  PARALLAX.— In  order  to  account  for  the  man- 
ner in  which  objects  are  represented  on  stereoscopic  images,  we 
may  suppose  two  transparent  plates  (MM,  fig.  188),  placed  in 


Fig.  188. 

front  of  the  eyes  at  the  place  which  the  stereoscopic  image  will 
occupy  later.  From  all  the  exterior  points  we  suppose  straight 
lines  directed  towards  the  eyes.  There  start  thus  from  each 
exterior  point  two  of  these  lines,  and  the  point  at  which  each 
of  these  straight  lines  cuts  the  corresponding  plate  is  the  repro- 
duction of  the  exterior  point.  If  the  latter  is  at  infinity  the 
two  straight  lines  are  parallel,  and  the  distance  BBj,  between 
the  two  points,  is  equal  to  the  base  line.  If  we  place  the  two 
transparent  stereoscopic  figures  one  over  the  other,  so  that  the 


384  PHYSIOLOGIC  OPTICS 

two  reproductions  of  the  same  point  situated  at  infinity  overlap, 
we  can  make  the  reproductions  of  all  the  points  situated  at  in- 
finity coincide  two  by  two.  —  If,  on  the  contrary,  the  exterior 
point  (C,  fig.  1  88)  is  not  at  infinity,  the  distance  between  the 
two  reproductions  is  less  than  that  of  the  eyes.  We  designate 
the  difference  by  the  name  stereoscopic  parallax.  The  parallax 
of  the  point  C  is  BD-f-B1D1r=E.  Designating  the  distance  be- 
tween the  two  eyes  by  b,  that  of  the  object  from  the  eyes  by 
AO=d,  and  the  distance  of  the  plate  from  the  eyes  by  g,  we 
have 


d  —  g  d  g  d 

The  parallax  increases,  therefore,  with  the  distance  between 
the  two  eyes,  and  it  is  the  greater  as  the  object  is  nearer  the 
observer. 

METHODS  OF  OBSERVING  THE  STEREOSCOPIC  IMAGES.  —  a.  Mak- 
ing the  visual  lines  parallel,  we  can  without  further  trouble  blend 
the  two  images  into  one,  which  appears  in  relief.  We  then  see 
three  images,  the  middle  one  of  which  gives  the  relief  ;  for  each 
eye  sees  not  only  the  image  which  is  intended  for  it,  and  which 
is  blended  with  that  of  the  other  eye,  but  also  the  image  which 
is  intended  for  the  other  eye;  we  can  eliminate  the  two  useless 
images  by  placing  the  hand  as  a  partition  between  the  eyes.. 
It  may  be  difficult  to  make  the  visual  lines  parallel  while  accom- 
modating for  a  quite  short  distance,  but  if  we  succeed  in  doing 
so,  the  illusion  is  as  perfect  as  with  the  stereoscope.  Frequently 
we  do  not  succeed  with  the  ordinary  stereoscopic  images  be- 
cause, being  intended  for  the  stereoscope  of  Brewster,  they  are 
calculated  for  too  long  a  base  line,  which  obliges  us  to  make  the 
visual  lines  diverge  in  order  to  fuse  them. 

We  can  also  look  at  the  images  by  directing  the  right  eye  to- 
wards the  image  of  the  left,  and  vice  versa,  so  that  the  visual 
lines  intersect  at  a  point  situated  in  front  of  the  image.  It  is 
then  necessary  to  place  on  the  left  the  image  intended  for  the 
right  eye,  under  penalty  of  seeing  the  relief  reversed,  if  the  sup- 
posed object  lends  itself  to  such  an  interpretation.  —  The  fused 


BINOCULAR  PERCEPTION  OF  DEPTH  335 

image  appears  diminished  and  situated  in  front  of  the  plane  of 
the  drawing,  at  the  point  of  intersection  of  the  visual  lines. 

b.  The  stereoscope  of  Wheatstone,  the  first  which  was  con- 
structed, is  composed  of  two  plane  mirrors  (bd  and  bdj,  form- 
ing a  right  angle  (fig.  189);  the  eye  O,  looks  into  the 'mirror 
on  the  right  at  the  image  of  the  drawing  Bt  Dlf  which  it  sees 
at  ffl ;  the  eye  O  sees  the  image  of  BD  at  the  same  place ;  the 
two  images  are  fused  into  a  single  one  presenting  relief.     In 
order  not  to  have  the  relief  reversed  or  pseudoscopic,  it  is  neces- 
sary to  present  to  the  left  eye  the  image  intended  for  the  right 
eye,  since  the  mirrors  reverse  the  images. 

c.  The  stereoscope  most  used  is  that  of  Brewster:  each  eye 
looks  through  a  prism  with  convex  surfaces,  the  apex  of  which 


Fig.  189. — Stereoscope  of  Wheatstone. 

is  turned  towards  the  nose.  The  glasses  produce  a  certain  mag- 
nification, and  their  prismatic  effect  renders  it  unnecessary  to 
make  the  visual  lines  parallel. 

We  can  replace  the  glasses  of  the  stereoscope  of  Brewster  by 
ordinary  convex  lenses,  by  decentering  them;  that  is  to  say,  by 
placing  them  so  that  the  distance  between  the  centers  of  the  two 
glasses  is  greater  than  the  distance  between  the  eyes. 


386 


PHYSIOLOGIC  OPTICS 


d.  When  the  image  represents  an  object  which  is  symmetrical 
in  relation  to  the  median  plane,  the  two  drawings  are  sym- 
metrical. We  can,  therefore, 
in  this  case  obtain  a  stere- 
oscopic effect  by  looking  with 
one  eye  at  an  ordinary  draw- 
ing, with  the  other  at  its  im- 
age by  reflection,  since  the  re- 
flection produces  a  sym- 
metrical image  of  it.  The 
most  convenient  way  is  to 
look  through  a  prism  with 
total  reflection. 

e.  Placing  a  prism  with  to- 

Fig.  190-Pseudoscope  of  Wheat-      tal  ration  in  front  of  each 

stone.  eye,  we  obtain  pseudoscopic 

relief  when  we  look  at  any  object,  providing  such  an  interpreta- 
tion is  possible.  A  cigar  is  thus  presented  as  a  hollow  leaf  of 
tobacco,  etc.  Wheat  stone  had  constructed  an  instrument  of  this 
kind  named  pseudoscope  (fig.  190). 

/.  The  telestereoscope  of  Helmkoltz  is  composed  of  four 
mirrors  arranged  as  we  see  in  figure  191.  The  rays  abf  a'b', 
coming  from  a  landscape,  are  reflected  by  the  large  mirrors 
towards  the  small  ones,  and  by  the  latter  towards  the  eyes.  We 
obtain  the  same  effect  as  if  the  eyes  A  and  B  were  in  the  posi- 
tion of  their  images  (AA  Bj)  produced  by  the  double  reflection. 
We  have  seen  that  binocular  relief  is  due  to  the  distance  which 
separates  the  two  eyes.  The  greater  this  distance  is  the  more 
pronounced  is  the  relief.  The  instrument  gives  relief  to  objects 
which,  under  ordinary  circumstances,  are  too  distant  to  give 
this  perception;  at  the  same  time  it  makes  them  appear  nearer 
and  smaller,  almost  as  if  we  looked  at  a  diminished  model  of 
them. 

g.  The  iconoscope  of  Javal  resembles  somewhat  an  inverted 
telestereoscope,  the  eyes  having  taken  the  place  of  the  object 
(a  and  c^),  and  the  object  that  of  the  eyes  (in  the  direction  of 
AB). 


BINOCULAR  PERCEPTION  OF  DEPTH 


387 


The  instrument  acts  as  if  the  eyes  were  very  near  each  other, 
at  c  and  cr  Looking  at  objects  through  this  instrument,  the 
relief  disappears:  the  object  appears  flat,  as  in  a  painting.  On 
the  contrary,  if  we  observe  an  engraving  through  the  instru- 
ment, it  presents  a  more  pronounced  relief  than  under  ordinary 
circumstances.  For,  the  binocular  vision  then  ceases  to  make 
us  observe  that  the  different  parts  of  the  image  are  in  the  same 
plane,  which  destroys  the  illusion.  Looking  through  the  icono- 
scope the  relief  is  more  marked  than  when  simply  closing  one 
eye. 


Fig.  191. — Telestereoscope  of  Helmholtz. 

h.  The  binocular  ophthalmoscope  of  Giraud-Teulon  is  analog- 
ous to  the  iconoscope.  The  mirrors  are  replaced  by  two  glass 
rhombohedra,  each  of  which  covers  half  of  the  opening  of  the 
ophthalmoscope.  As  in  the  preceding  case,  the  rays  reach  the 
eye  after  a  double  reflection  on  the  small  surfaces  of  the  rhom- 
bohedron.  The  instrument  acts  as  if  the  eyes  were  at  cc1  (fig. 
192). 


388 


PHYSIOLOGIC  OPTICS 


i.  We  draw  the  two  figures,  over  each  other,  one  with  red 
lines,  the  other  with  blue  lines.  Looking  through  a  red  glass 
we  do  not  see  the  red  lines,  and  vice  versa. — If  we  look  at  these 
anaglyphs,  placing  a  red  glass  in  front  of  one  eye  and  a  blue 


Fig.  192. — Binocular  ophthalmoscope  of  Giraud-Teulon. 

glass  in  front  of  the  other,  we  obtain  a  stereoscopic  effect. 
Changing  the  glasses  the  relief  is  reversed,  if  the  nature  of  the 
object  permits  such  an  interpretation  (d'  Almeida). 

132.  The  effect  of  the  stereoscope  is  to  give  an  idea  of  the 
third  dimension,  such  as  no  other  representation  can  give  of  it. 
Its  use  has  become  especially  popular  since  stereoscopic  photo- 
graphs have  been  made,  for  though  we  can  make  stereoscopic 
drawings  of  stereometric  figures,  etc.,  it  is  impossible  to  make 
them  of  a  landscape  so  that  the  reproduction  may  be  exact. 
Dove  used  the  stereoscope  to  see  whether  a  bank  note  was  false, 
by  placing  it  in  one  of  the  fields  and  putting  a  genuine  note  in 
the  other.  If  it  was  false  he  saw  some  of  the  letters  leave  the 
plane  of  the  paper,  for  it  is  impossible  to  make  an  entirely 
exact  counterfeit  of  an  engraving,  and  the  least  difference  in 
the  distance  of  the  letters  produces  relief. 

STEREOSCOPIC  LUSTRE. — Under  ordinary  circumstances  there 
are  usually  formed  only  in  one  eye  images  of  the  same  objects 


BINOCULAR  PERCEPTION  OF  DEPTH  389 

as  in  the  other;  as  long  as  we  place  in  the  stereoscope  images 
of  real  objects  only,  we  simply  see  the  relief.  I  have  already 
said  that,  in  the  case  of  the  controlled  reading  of  Javal,  we  see 
at  the  same  place  the  stick  and  the  letters  which  it  should  con- 
ceal. The  observer  gets  over  the  difficulty  by  supposing  the  stick 
transparent.  Another  interpretation  of  the  same  kind  is  known 
as  stereoscopic  lustre  (Dove}.  If  we  draw  one  of  the  stereo- 
scopic figures  with  black  lines  on  a  white  ground,  the  other 
with  white  lines  on  a  black  ground,  we  observe  that  the  fused 
image  presents  a  certain  brightness,  almost  as  if  it  was  covered 
with  a  layer  of  plumbago.  Replacing  the  black  surfaces  by 
colored  surfaces,  we  sometimes  obtain  the  metallic  lustre. — 
Every  bright  body,  in  fact,  sends  back  two  kinds  of  light : 
regularly  reflected  white  light  and  diffuse  light  which  has  the 
color  of  the  body  itself.  When,  in  the  stereoscope,  we  see  at 
the  same  place  white  light  and  colored  light,  the  contradiction 
is  explained  by  supposing  that  the  object  we  look  at  is  bright. 

ANTAGONISM  OF  THE  VISUAL  FIELDS. — When  the  images  v 
placed  in  the  two  fields  are  so  different  that  they  cannot  be 
fused,  as,  for  example,  if  we  present  to  one  eye  horizontal  lines 
and  to  the  other  vertical  lines,  we  observe  the  phenomenon 
known  as  antagonism  of  the  visual  fields:  it  is  sometimes  one, 
sometimes  the  other  field  which  predominates,  and  while  one 
predominates  the  other  is  suppressed;  we  do  not  see  it  at  all. 
It  is  not  the  field  of  the  same  eye  which  predominates  every- 
where ;  the  common  field  is  composed  of  parts  belonging  to  either 
eye.  When  one  of  the  fields  has  predominated  at  one  place  for 
some  time,  the  appearance  changes,  the  other  field  getting  the 
upper  hand.  The  change  often  takes  place  under  an  external 
influence;  a  winking  of  the  eyelids  or  a  change  in  the  direction 
of  the  look  sometimes  suffices  to  bring  it  about.  Furthermore, 
the  phenomena  vary  much  according  to  the  objects. 

If  we  present  to  each  eye  outline  pictures  which  do  not  cor- 
respond to  each  other,  drawn  on  a  uniform  ground,  but  different 
for  both  eyes,  we  observe  that  the  ground  of  each  field  pre- 
dominates near  the  picture  which  belongs  to  it.  The  following 
experiment  demonstrates  this  fact  in  a  quite  striking  manner. 


390 


PHYSIOLOGIC  OPTICS 


We  draw  in  one  of  the  fields  a  large  black  vertical  bar,  in  the 
other,  another  similar  but  horizontal  bar:  on  blending  the  fields 
the  bars  form  a  cross  (fig.  193),  the  middle  of  which,  situated 
at  the  point  where  the  two  bars  cross,  is  black;  the  parts  next 
to  the  middle  are  whitish,  because  the  outline  picture  makes  the 
white  ground  predominate.  The  extremities  of  the  arms  appear, 
on  the  contrary,  almost  as  black  as  the  middle,  in  spite  of  the 
superimposing  of  the  white  on  the  other  field. 

J  In  making  this  experiment,  we  experience  a  difficulty  in  fixing 

the  images  on  each  other:  the 
vertical  arm  glides  on  the  hori- 
zontal arm.  This  is  due  to  the 
fact  that  there  are  no  common 
vertical  lines  which  can  guide  us 
for  the  degree  of  convergence. 
On  account  of  their  import- 
ance for  convergence  we  desig- 
nate the  vertical  lines  as  the 
dominating  outlines.  To  prevent 
the  two  figures  from  gliding  on 
each  other,  we  place  at  the  mid- 
Fig.  193.— After  Helmholtz.  die  of  each  line  a  small  white 

cross.  The  tendency  to  fuse 

these  small  crosses  suffices  to  fix  the  vertical  bar  at  the  middle 

of  the  horizontal  bar. 


When  the  two  fields  have  not  the  same  color,  we  generally 
observe  antagonism  of  the  visual  fields.  I  have  thus  arranged 
the  experiment  with  colored  shadows  (page  289)  so  as  to  have 
one  of  the  shadows  in  each  field  of  the  stereoscope.  On  blend- 
ing them  it  was  sometimes  one,  sometimes  the  other  color  which 
predominated.  I  repeated  the  experiment  with  several  of  my 
pupils,  none  of  whom  succeeded  in  seeing  the  gray  shadow. — 
There  are  authors,  however,  who  claim  to  have  obtained  the 
color  of  the  mixture;  the  phenomenon  is  then,  perhaps,  of  the 
same  order  as  stereoscopic  lustre. 


BINOCULAR  PERCEPTION  OF  DEPTH  391 

133.  Identical  Points  of  the  Retinae.— We  say  that  one  point 
of  a  retina  is  corresponding  to,  or  identical  with,  a  point  of  the 
other  one,  when  the  images  of  the  same  exterior  point  falling 
on  these  two  retinal  points  are  blended  into  a  single  image.  If, 
in  the  second  eye,  the  image  is  formed  on  any  other  point,  it 
is  not  blended  with  that  of  the  first  eye :  the  point  is  seen  double. 

It  is  evident  that  the  two  foveas  are  corresponding  points, 
since  the  object  fixed  is  always  single.  To  find  the  other  identical 
points,  Johannes  Muller  has  given  the  following  rule.  We  sup- 
pose the  retina  divided  into  quadrants  by  a  horizontal  meridian 
and  a  vertical  meridian,  both  passing  through  the  fovea.  The 
position  of  each  point  is  then  determined,  as  on  a  terrestrial 
globe,  by  its  longitude  and  latitude  in  relation  to  these  two 
meridians.  Two  points  having  the  same  longitude  and  latitude 
are  identical.  The  rule  of  Muller  agrees  with  that  which  we 
have  laid  down  in  chapter  XXI,  according  to  which  an  object 
is  seen  single  when  the  two  eyes  see  it  in  the  same  direction  in 
relation  to  the  point  fixed. 

The  researches  of  Volknwmn  have  shown  that  the  law  of 
Muller  is  not  wholly  exact,  and  that  it  is  necessary  to  replace 
the  vertical  meridians  by  apparently  vertical  meridians,  which, 
for  a  person  standing  upright  and  looking  towards  the  horizon, 
converge  about  two  degrees  in  the  downward  direction,  so  as 
to  almost  meet  at  the  ground  (see  page  356).  We  then  suppose 
the  retina  divided  by  circles  parallel  to  this  meridian  as  well  as 
to  the  horizontal  meridian,  and  the  law  of  Muller  is  applicable. 
— Placing  in  each  field  a  really  vertical  line,  these  lines  appear 
to  converge  upwards  and  must,  consequently,  cross  if  we  try 
to  blend  them.  In  order  that  the  experiment  may  succeed  it  is 
necessary,  however,  to  arrange  them  so  that  one  line  may  be 
white  on  a  black  ground,  the  other  black  on  a  white  ground. 
Otherwise  the  lines  are  blended  nevertheless. 

THEORIES  ON  THE  NATURE  OF  IDENTITY. — The  question  of 
knowing  why  two  points  are  corresponding  while  two  others  are 
not,  has  been  much  discussed.  Most  of  the  advocates  of  the 
theory  of  identity  suppose  that  there  exists  an  anatomical  rela- 
tion between  the  two  corresponding  points.  They  suppose  that 


392  PHYSIOLOGIC  OPTICS 

the  nerves  conducting  the  impressions  of  two  corresponding 
points  unite,  on  their  way  to  the  chiasma,  into  one  which  con- 
ducts the  impression  to  the  brain.  This  idea  was  already  ex- 
pressed by  Galien,  and  has  been  confirmed  by  Newton,  Wollaston 
and  others.  The  so-called  theory  of  projections  is  expressed 
almost  as  we  have  described  it  in  chapter  XXI :  a  point  on  the 
left  retina,  situated  10  degrees  to  the  left  of  the  jovea,  localizes 
its  impression  at  10  degrees  to  the  right  of  the  point  of  fixa- 
tion; the  point  situated  at  10  degrees  to  the  left  of  the  right 
jovea  localizes  its  impression  in  the  same  direction;  and  as  the 
two  impressions  are  localized  in  the  same  direction,  they  are 
blended  into  one.  The  identity  of  the  two  foveas  might  be  a 
result  acquired  by  experience.  This  theory  has  been  upheld  by 
Kepler,  Porterfield  and,  under  an  erroneous  form,  by  Giraud- 
Teulon. 

Immediately  after  the  invention  of  the  stereoscope  and  the 
studies  of  the  production  of  relief  to  which  this  invention  gave 
rise,  there  was  an  inclination  to  abandon  the  idea  of  correspond- 
ing points,  for  the  stereoscopic  experiments  seem  opposed  to 
what  we  have  said  on  these  points.  Indeed,  let  us  look  in  the 
stereoscope  at  a  representation  of  the  two  points  A  and  B,  both 
situated  in  the  median  plane,  and  fix  the  more  distant  A.  The 
images  of  B  are  not  formed  on  two  corresponding  points,  since 
in  one  eye  its  image  is  to  the  right,  in  the  other  to  the  left  of 
the  jovea.  Nevertheless,  we  see  it  single  and  in  relief;  that 
is  to  say,  nearer  than  A. — On  account  of  this  apparent  contra- 
diction, Wheatstone  inclined  towards  the  theory  of  projections. 
In  despair  of  a  better  explanation,  th'e  advocates  of  the  theory 
of  identity  supposed  that  a  point  of  one  of  the  retinae  does  not 
correspond  to  a  point,  but  to  a  small  surface  of  the  other 
(Panum).  An  image  falling  on  the  point  of  the  first  retina  could 
then  become  blended,  either  without  relief,  with  an  image  formed 
at  the  middle  of  the  small  surface  of  the  other,  or  with  relief, 
with  an  image  formed  on  a  more  peripheral  point  of  the  small 
surface.  But,  under  this  form,  the  theory  of  identity  was  not 
tenable ;  it  would  be  necessary,  indeed,  to  suppose  that  the  same 
two  points  could  be  sometimes  corresponding,  sometimes  not 


BINOCULAR   PERCEPTION   OF  DEPTH  393 

corresponding,  which  is  scarcely  admissible.  The  question  was 
cleared  up  only  by  the  labors  of  Javal. 

THEORY  OF  JAVAL  ON  THE  PRODUCTION  OF  RELIEF.— This 
theory  calls  especially  for  two  factors,  the  neutralization  (par- 
tial suppression  of  one  of  the  images)  and  the  influence  of  the 
ocular  movements,  on  which  Briicke  had  already  insisted.  In 
chapter  XXI  reference  was  made  to  the  suppression  of  one  of 
the  images,  which  takes  place  when  different  images  are  formed 
on  two  corresponding  parts  of  the  retinae.  We  then  see,  some- 
times the  image  of  one  eye,  sometimes  that  of  the  other,  and 
while  we  see  the  image  of  one  eye,  the  corresponding  part  of 
the  image  of  the  other  disappears  absolutely.  In  normal  per- 
sons the  suppression  especially  manifests  itself  alternately  for 
both  eyes,  under  the  form  of  antagonism  of  the  visual  fields;  in 
strabismic  patients,  on  the  contrary,  we  often  have  occasion 
to  observe  the  constant  neutralization  of  a  great  part  of  the 
visual  field  of  one  eye. 

Briicke  was  the  first  who  insisted  on  the  great  importance  of 
the  ocular  movements  for  the  perception  of  relief.  Anyhow,  it 
is  certain  that  without  them  we  could  have  only  a  very  vague 
notion  of  it.  Looking  into  a  stereoscope,  especially  if  the  images 
are  difficult  to  fuse,  it  is  only  after  I  have  permitted  my  look 
to  wander  for  some  time  on  the  figures,  fusing  sometimes  the 
images  of  the  distant  objects,  sometimes  those  of  the  near  ob- 
jects, that  relief  appears  to  me.  As  long  as  the  sensation  of 
relief  is  not  produced  I  see  double,  sometimes  the  near  objects, 
sometimes  the  distant  ones;  but  at  the  moment  when  relief 
appears,  I  see  all  of  them  single.  Certain  authors  claim  that  they 
have  observed  relief  by  illuminating  the  stereoscopic  images  with 
an  electric  spark,  the  duration  of  which  light  is  so  short  that 
all  ocular  motion  is  necessarily  excluded.  This  would  certainly 
be  impossible  in  my  case,  for  there  always  elapses  a  certain  time 
before  the  real  illusion,  which  does  not  prevent  me  from  being 
able  to  form  all  at  once  a  vague  notion  of  relief. 

According  to  Javal,  it  is  necessary,  indeed,  to  distinguish  be- 
tween the  idea  of  relief,  which  is  produced  by  the  fact  that  we 
see  near  objects  in  double  crossed  images,  and  the  measurement 


394 


PHYSIOLOGIC  OPTICS 


of  relief,  which  depends  on  the  sensation  of  the  degree  of  in- 
nervation  necessary  to  converge  towards  the  near  object.     To 
account  for  the  manner  in  which  we  come  to  obtain  the  sensa- 
tion of  relief,  it  is  preferable  to  use  images  which  are  quite 
difficult  to  blend,  the  stereoscopic  parallax  of  the  objects  repre- 
sented being  quite  strong.    We  immediately  fuse  the  images  of 
distant  objects,  and  all  the  others  appear  in  double  images.    We 
then  allow  the  look  to  stray  on  the  figure,  which  forces  con- 
vergence more  or  less,  according  as  the  object  is  represented 
more  or  less  distant.     After  having  continued  thus  for  some 
time,  relief  manifests  itself  almost  in  the  same  way  as  we  can 
with  closed  eyes  obtain  a  very  distinct  idea  of  the  form  of  an 
object  by  feeling  it  with  the  fingers. 
At  the  same  time  that  relief  appears, 
the    double    images    disappear;   the 
image  of  one  or  other  eye  is  sup- 
pressed.    If  one  of  the  eyes  plays 
the  part  of  the  directing  eye   (see 
page  371 )    it  is  usually  the  images 
of   the   other   eye    which    are   sup- 
pressed, unless  the  image  of  the  pre- 
ponderating eye  is  much  more  peri- 
pheral than  that  of  the  other.     In 
cases  in  which  this  preponderance  is 
not    developed,    the    double    images 
seem  to  appear  following  the  law  of 
Javal:  we  suppress  that  one  of  the 
images  which  occupies  the  smallest 
retinal  surface.    We  can  account  for 
the  manner  in  which  we  suppress 
the  images  by  looking  at  a  rule  which  is  held  obliquely  before 
the  eyes,  so  that  it  presents  a  greater  surface  to  one  eye  than 
to  the  other.    Whether  it  occupies  the  position  AA  (fig.  194),  or 
the  position  BB,  it  seems  to  me,  seen  binocularly,  to  have  the 
same  appearance  as  when  I  close  the  left  eye.    Persons  in  whom 
the  preponderance  of  one  eye  is  not  developed  see  the  rule 
binocularly,  as  it  is  presented  to  the  left  eye,  if  it  occupies  the 


Fig.  194. 


BINOCULAR  PERCEPTION  OF  DEPTH  395 

position  AA.     In  the  position  BB  they  see  it,  on  the  contrary, 
as  it  presents  itself  to  the  right  eye. 

The  discussion  of  the  two  theories  of  binocular  vision,  that 
of  identity  and  that  of  projections,  has  not  yet  closed.  The 
explanation  of  Javal  is  applicable  in  reality  as  well  to  one  as  to 
the  other.  We  can  imagine  the  projection  learned  by  experience ; 
and  even  the  fact  of  always  projecting  the  images  of  the  two 
foveas  at  the  same  place,  the  foundation  stone  of  binocular  vision, 
may  be  something  learned.  It  is,  perhaps,  the  superiority  of 
the  fovea,  as  to  visual  acuity,  which  causes  us  to  always  bring 
the  images  of  the  object  which  interests  us  to  form  themselves 
on  both  f oveas,  and  we  may  thus  have  been  led  to  always  localize 
the  impression  of  the  two  foveas  at  the  same  place.  On  the 
other  hand,  the  advocates  of  the  theory  of  identity  take  their 
stand  on  the  anatomical  observations  of  the  semi-decussation  in 
the  chiasma,  and  especially  on  comparative  anatomy,  which 
shows  that  in  many  animals — fish,  for  example — whose  eyes  are 
placed  so  as  not  to  have  a  common  visual  field,  the  optic  nerves 
cross  completely.  Clinical  observations  in  hemianopsia,  especially 
those  of  partial  hemianopsia,  are  a  further  argument  in  favor 
of  this  theory.  The  study  of  the  vision  of  strabismic  patients, 
which  is  perhaps  the  best  means  of  deciding  the  question  finally, 
shows,  as  we  shall  see  in  the  following  chapter,  that,  in  conse- 
quence of  a  false  position  of  the  eyes,  there  may  be  developed 
a  kind  of  correspondence  between  two  retinal  points  which, 
under  ordinary  circumstances,  are  not  corresponding;  but  this 
relation  never  assumes  the  character  of  true  binocular  vision  with 
fusion,  and  it  sometimes  suffices,  in  a  person  who  has  squinted 
since  childhood,  to  place  the  eyes  in  an  approximately  correct 
position,  in  order  that,  in  the  course  of  a  fortnight,  correct  pro- 
jection may  gain  the  upper  hand. 

Bibliography. — Wheatstone  (C.).  Contributions  to  the  Physiology  of 
Vision.  On  some  Remarkable  and  hitherto  Unobserved  Phenomena  of 
Binocular  Vision.  Phil,  trans.,  1838,  II,  p.  371-394.— Wheatstone  (C.). 
Contribution  to  the  Physiology  of  Vision,  II.  Phil.  Mag.,  4,  III,  p.  149- 
152  and  p.  504-523. — Brewster  (D.).  The  stereoscope.  London,  1858. — 
Helmholtz  (H.).  Das  TelestereosTcop.  Pogg.  Ann.,  CI,  p.  494-CII,  p.  167.— 


396  PHYSIOLOGIC  OPTICS 

Javal  (E.).  Sur  un  instrument  nomme  Iconoscope,  destine  d  donner  du 
relief  aux  images  planes  examinees  avec  les  deux  yeux.  Report,  LXIII,  927. 
— Javal  (E.).  De  la  neutralisation  dans  Vacte  de  la  vision.  Ann.  dfoc., 
LIV,  p.  5. — Miiller  (Johannes).  Beitrdge  zur  vergleichende  Physiologie  des 
Gesitchtssinnes.  Leipzig,  1826,  p.  191. — Volkmann  (A.  W.).  Physiologische 
Untersuchungen  im  Gebiete  der  Optik,  II.  Leipzig,  1864. — Newton  (J.). 
Opticlcs,  1717,  p.  320. — Panum  (P.  L.).  Physiologische  Untersuchung  uber 
das  Sehen  wvit  zwei  Augen.  Kiel,  1858. — Briicke.  Ueber  die  stereoscopische 
Erscheinungen.  Miiller 's  Archiv  fiir  Anat.  u.  PhysioL,  1841,  p.  459. — Nagel 
(A.).  Das  Sehen  mit  zwei  Augen  und  die  LeJire  von  den  identischen  Netz- 
hautstellen.  Leipzig,  1861. — Javal  (E.).  Manuel  du  straMsme.  Paris, 
Masson,  1896. 


CHAPTER   XXIV 

STRABISMUS 

134.  Different  Forms  of  Strabismus. —  We  say  that  there  is 
strabismus  when  the  two  visual  lines  do  not  intersect  at  the  point 
fixed.  The  image  of  the  point  fixed  is  not,  therefore,  formed 
on  the  two  joveas,  and  since  the  two  foveas  are  always  corre- 
sponding points,  there  is  no  binocular  vision.  One  might,  there- 
fore, define  strabismus  as  the  condition  in  which  binocular  vision 
is  wanting,  at  least  at  certain  moments  or  for  certain  directions 
of  the  look.  It  must  be  observed,  however,  that  we  may  meet 
with  cases  in  which  the  visual  lines  have  the  proper  direction, 
at  least  apparently,  but  in  which  binocular  vision  is,  nevertheless, 
wanting;  this  case  often  presents  itself  in  persons  affected  with 
strabismus,  who  have  undergone  a  successful  operation.  It  is 
also  customary  to  speak  of  strabismus  when  one  eye  deviates, 
even  if  it  is  completely  blind.  The  study  of  strabismic  patients 
is  very  important  for  different  questions  of  physiologic  optics. 

We  distinguish  two  forms  of  strabismus :  paralytic  strabismi^, 
due  to  a  paralysis  of  one  or  more  muscles,  and  concomitant 
strabismus,  which,  in  the  great  majority  of  cases,  is  due  to  the 
defect  of  innervation  (Hansen-Grut) .  The  symptoms  by  which 
we  make  the  differential  diagnosis  between  these  two  forms  of 
strabismus  are  well  known.  They  have  passed  from  the  classic 
memoir  of  Graefe  into  all  treatises  of  ophthalmology.  In  cases 
of  paralytic  strabismus  the  excursion  of  the  eye  is  less  on  the 
side  of  the  paralyzed  muscle,  and  the  secondary  deviation  is 
greater  than  the  primary.  Patients  present  diplopia,  either  spon- 
taneously, or  more  especially  if  we  examine  them  with  a  candle 
and  a  colored  glass.  The  distance  between  the  two  images  in- 
creases when  the  look  is  directed  towards  the  side  of  the  dis- 
eased muscle,  and  it  is  the  image  of  the  diseased  eye  which  is 
farthest  away  in  this  direction. 

When  the  patient  closes  the  healthy  eye  and  looks  towards 

397 


398  PHYSIOLOGIC  OPTICS 

an  object  situated  on  the  side  of  the  diseased  muscle,  the  pro- 
jection is  false;  for,  as  it  is  necessary,  on  account  of  the  paresis, 
to  use  a  stronger  innervation  to  bring  the  eye  to  fix  the  object, 
the  patient  thinks  that  this  object  is  situated  more  to  one  side 
than  it  really  is,  and  when  he  wants  to  grasp  it  quickly  he  brings 
the  hand  too  far  to  that  side.  I  have  already  observed  (page 
367)  the  importance  of  this  observation  to  demonstrate  that  we 
judge  the  direction  of  the  look  above  all  by  the  degree  of  in- 
nervation used  to  bring  it  into  this  direction. 

CONCOMITANT  STRABISM'US. — When  we  speak  of  strabismus 
without  other  qualification  it  is  generally  this  form  that  we 
mean. — In  this  strabismus  the  deviation  is  almost  the  same  for 
all  directions  of  the  look,  except  that  generally  the  convergence 
is  more  pronounced  for  the  downward  than  for  the  upward  look. 
The  secondary  deviation  is  equal  to  the  primary  deviation.  The 
patient  does  not  complain  of  diplopia,  but  we  may  always  bring 
it  about  by  the  means  which  I  shall  describe  forthwith.  The 
distance  between  the  two  images  is  the  same  everywhere,  to 
whichever  side  the  patient  looks.  The  simplest  means  of  diag- 
nosing strabismus  is  to  make  the  patient  fix  an  object,  the  finger 
of  the  observer,  for  example.  If  one  of  the  eyes  seems  to 
deviate,  we  cover  the  other,  and  if  the  former  then  makes  a 
movement  to  fix,  it  was  deviated:  strabismus  is,  therefore, 
proved.  This  examination  must  be  repeated  for  a  distant  ob- 
ject. If  we  do  not  discover  strabismus  by  this  means,  it  may, 
nevertheless,  happen  that  the  patient  has  it,  but  in  a  very  slight 
degree,  or,  in  other  words,  that  he  has  no  binocular  vision;  we 
may,  in  this  case,  place  a  prism,  apex  inwards,  in  front  of  the 
eye.  If  there  is  binocular  vision  the  eye  makes  a  movement  of 
convergence  to  neutralize  the  effect  of  the  prism  (Graefe). — If 
the  strabismus  is  periodic  we  can  sometimes  discover  it  by  mak- 
ing the  patient  fix  a  very  small  object,  a  word  printed  in  very 
small  type,  for  example;  the  patient  is  obliged  to  accommodate 
to  distinguish  the  word,  and  the  effort  of  accommodation  may 
then  cause  strabismus. 

LATENT  STRABISMUS. — In  order  to  see  whether  there  is  latent 
strabismus,  we  make  the  patient  fix  the  finger  of  the  observer; 


STRABISMUS  399 

we  cover  one  eye  and  examine,  on  uncovering  it,  whether  the 
eye  deviated  under  the  hand  and  whether  it  straightened  itself 
in  order  to  fix.  If  the  deviating  eye  does  not  straighten  itself, 
the  strabismus  has  become  manifest;  if  it  does  straighten  itself, 
it  is  latent. — According  to  Graefe,  we  make  the  patient  observe 
a  long  vertical  line  which  has  at  the  middle  a  black  spot,  or, 
which  is  preferable,  a  candle,  while  we  place  in^front  of  one 
of  his  eyes  a  prism,  apex  upwards.  If  there  is  latent  strabis- 
mus, the  patient  sees  two  objects  placed  exactly  one  above  the 
other  (if  the  apex  of  the  prism  forms  a  horizontal  line).  If 
not,  there  is  latent  strabismus,  and  we  can  then  measure  the 
degree  of  it  by  placing  the  prism  of  Cretes  before  the  other  eye 
and  finding  the  degree  of  this  prism  which  makes  one  image 
appear  above  the  other.  We  can  also  use  the  Maddox  test,  etc. 
Javal  placed  a  ground  glass  lens  before  one  of  the  eyes  of  the 
patient;  this  glass  prevents  the  eye  which  it  covers  from  dis- 
tinguishing anything,  while  the  observing  eye  sees  the  covered 
eye  sufficiently  well  to  judge  of  its  position. 

Making  the  examination  in  this  way,  we  find,  in  many  people, 
a  slight  degree  of  latent  divergent  strabismus  for  near  vision. 
This  condition  is  often  designated  as  insufficiency  of  the  internal 
recti.  This  expression  is  ill-chosen  and  should  be  discontinued. 
The  internal  recti  are  not  weaker  than  in  the  normal  eyes,  as 
Hansen-Grut  has  shown,  for,  otherwise  this  weakness  ought  to 
manifest  itself  also  for  the  associated  movements.  If  the  right 
internal  rectus  were  really  weaker  than  in  the  normal  state,  we 
should,  when  looking  to  the  left,  see  the  phenomena  appear 
which  characterize  paresis  of  the  right  internal  rectus,  which  is 
by  no  means  the  case.  It  is  not  in  the  muscles,  it  is  in  the  in- 
nervation  of  convergence  that  we  must  search  for  the  cause  of 
this  deviation.  We  might,  therefore,  speak  of  an  insufficiency 
of  convergence,  but  this  also  would  be  a  bad  expression,  for 
many  patients  affected  with  this  deficiency  can  converge  as  well 
as  normal  persons;  it  is  only  the  stimulus  of  convergence  that 
is  wanting,  (i) 


(1)    [In  this  country  Stevens'  nomenclature  has  been  generally  accepted.     Ac- 
cording to  him  this  condition  is  called  exophoria.] — W. 


400  PHYSIOLOGIC  OPTICS 

135.  Measurement  of  Strabismus. —  i°    We    cover    the    good 
eye;  the  strabismic  eye  straightens  itself,  and  we  value,  in  milli- 
meters, the  extent  of  the  displacement  of  the  cornea. 

2°  Javal  has  proposed  to  measure  the  deviation  in  degrees  by 
means  of  the  perimeter.  He  places  the  patient  so  that  the 
strabismic  eye  is  in  front  of  the  point  of  fixation  of  the  peri- 
meter. The  patient  fixes  this  point  with  his  good  eye.  The 
observer  then  moves  a  candle  along  the  arc  of  the  perimeter, 
sighting  in  the  direction  of  this  candle  towards  the  strabismic 
angle.  He  finds  the  position  in  which  the  corneal  image  is  at 
the  middle  of  the  pupil,  which  indicates  approximately  the  direc- 
tion of  the  visual  line  of  the  strabismic  eye.  In  the  keratoscopic 
arc  of  de  Wecker,  the  candle  is  replaced  by  a  white  mire,  and 
at  the  point  of  fixation  is  a  small  mirror  in  which  is  reflected  a 
distant  object  which  serves  as  the  point  of  fixation. 

3°  We  can  use  the  distance  of  the  two  images  as  a  measure 
of  the  strabismus  if  there  is  diplopia.  We  can  measure  this  dis- 
tance with  the  prism  of  Cretes,  or  by  projecting  the  images  on 
a  wall  provided  with  a  graduation  in  degrees  (Hirschberg,  Lan- 
dott)  or  on  a  Prentice  scale. 

The  deviation  often  varies  much  with  the  distance  of  the  ob- 
ject fixed.  It  may  also  be  useful  to  determine  the  deviation  at 
different  distances,  at  4  meters  and  at  25  centimeters,  for  ex- 
ample, as  Schioets  has  proposed. 

136.  The  etiology  of  concomitant  strabismus  is   a   quite   com- 
plex question  on  which  opinions  are  still  divided.     Boehm  dis- 
covered the  relation  which   exists  between  hypermetropia  and 
convergent  strabismus,  and  Danders,  in  a  general  way,  announced 
the  part  that  the  anomalies  of  refraction  play  in  the  etiology  of 
strabismus.    This  influence  cannot  be  denied,  and  it  is  especially 
striking  for  convergent  strabismus.     In  my  extensive  compila- 
tion of  statistics  of  young  conscripts  (see  page  101)  there  were 
42  cases  of  convergent  strabismus,  of  whom  31   were  hyper- 
metropes,  7  emmetropes  and  4  myopes ;  that  is  to  say,  that  about 
70   per   cent,   of   the   persons   squinting   inwards    were   hyper- 
metropes.    But,  on  the  other  hand,  there  were  in  all  301  hyper- 


STRABISMUS  401 

metropes  (of  2  dioptrics  or  more) ;  only  a  very  small  minority 
of  the  hypermetropes  squint,  therefore. 

The  manner  in  which  Bonders  explained  the  relation  between 
convergent  strabismus  and  hypermetropia  is  well  known.  When 
an  emmetrope  fixes  a  near  object,  it  is  above  all  the  necessity 
of  seeing  it  single  which  regulates  the  position  of  his  eyes.  But, 
if  we  cover  one  of  the  eyes,  this  need  no  longer  exists,  and, 
nevertheless,  the  observed  person  generally  continues  to  con- 
verge towards  the  point  fixed;  this  is  due  to  the  relationship 
which  exists  between  accommodation  and  convergence.  Even 
if  the  observed  person  is  sufficiently  myopic  to  make  it  unneces- 
sary for  him  to  accommodate  for  the  object,  the  covered  eye 
converges,  nevertheless,  pretty  exactly  for  the  object.  This  is 
due  to  what  Hansen-Grut  termed  sensation  of  the  distance; 
knowing  that  the  object  is  at  a  short  distance  away,  the  patient 
converges  because  he  is  accustomed  to  do  so  in  the  interest  of 
binocular  vision,  even  in  a  case  in  which  this  interest  no  longer 
exists. 

These  three  factors  regulate  the  degree  of  convergence  to  be 
used.  Under  ordinary  circumstances,  it  is  the  first  factor  which 
is  of  most  importance;  but,  in  cases  of  hypermetropia,  it  may 
happen  that,  in  order  to  sustain  his  accommodation,  the  patient 
converges  more  than  is  necessary  for  fusion.  He  then  sacrifices 
his  binocular  vision  to  obtain  distinct  vision  with  one  eye  only, 
and  this  happens  with  special  ease  when  the  vision  of  the  other 
eye  is  diminished  for  one  reason  or  another  (opacities  of  the 
cornea,  astigmatism,  etc.).  In  a  certain  number  of  cases  we 
find  vision  greatly  diminished  without  any  perceptible  reason. 
We  cannot  yet  say  whether  this  diminution  is  a  consequence  of 
strabismus  (amblyopia  ex  anopsia),  or  whether  it  is  not  rather 
a  cause  of  strabismus,  due  to  a  congenital  anomaly. 

If  we  thus  explain  why  a  hypermetrope  may  become  strabis- 
mic,  we  cannot  well  understand  why  the  great  majority  of  hy- 
permetropes do  not  squint.  They  often  seem  to  have  quite  as 
much  reason  to  squint  as  strabismic  patients.  Javal  supposes 
that  strabismus  has  developed  under  the  influence  of  paresis  of 
the  accommodation  which  is  cured  later.  The  existence  of  such 


402  PHYSIOLOGIC  OPTICS 

paresis  is  certainly  hypothetical,  but  it  would  very  well  explain 
the  origin  of  strabismus;  the  parents  of  strabismic  children  are 
quite  frequently  affected  with  convulsions,  intestinal  worms, 
which  might  have  produced  nervous  troubles,  etc.  According  to 
de  Wecker,  a  certain  number  of  cases  of  convergent  strabismus 
might  be  due  to  a  paralysis  of  one  of  the  external  recti  acquired 
during  infancy.  Paralytic  strabismus  would  be  transformed 
later  into  concomitant  strabismus. 

Myopia  plays,  in  the  production  of  divergent  strabismus,  a 
less  important  role  than  hypermetropia  in  the  production  of  con- 
vergent strabismus.  As  the  myope  does  not  accommodate  at 
all,  or  only  slightly  for  near  objects,  one  of  the  factors  which 
sustains  convergence  is  wanting.  If  the  eyes  are  very  unequal, 
there  may  readily  follow  a  divergent  strabismus  relative  to  near 
objects.  On  the  other  hand,  distant  vision  is  so  diffuse  for  the 
more  imperfect  eye  that  binocular  vision  is  of  little  usefulness, 
and  this  eye  then  easily  deviates  outwards.  Generally  speaking, 
every  eye,  the  vision  of  which  is  destroyed  or  greatly  diminished, 
has  a  tendency  to  deviate  outwards. — In  very  rare  cases  we  meet 
in  myopes  a  special  form  of  convergent  strabismus. 

The  ideas  on  the  nature  of  strabisums  are  much  divided. 
Most  authors  find  the  cause  of  strabismus  in  the  muscles,  for 
instance,  v.  Graefe  ("excess  of  average  contraction"),  Schweig- 
ger  ("excess  of  elasticity  of  the  muscles"),  etc.  Others,  Alfred 
Graefe  and  Javal,  for  instance,  attribute  periodic  strabismus  and 
the  variable  part  of  permanent  strabismus  to  innervation,  while 
they  suppose  that  the  permanent  part  is  due  to  consecutive 
muscular  alterations.  The  theories  which  attribute  the  vast 
majority  of  cases  of  strabismus  to  a  defect  of  innervation  are 
beginning  to  gain  ground.  They  have  been  advocated  by  Stell- 
wag,  Rahlmann,  Hansen-Grut  and  Parinaud.  The  theory  of 
Hansen-Grut  seems  to  me  to  adapt  itself  best  to  the  phenomena. 

According  to  this  author,  the  whole  muscular  theory  collapses 
before  the  following  observation.  Suppose  a  left  convergent 
strabismus  of  6  mm. :  if  this  strabismus  had  a  muscular  origin, 
it  would  be  necessary  that  the  limit  of  excursion  outwards  of 
the  left  eye  would  be  displaced  inwards  6  mm.  But  we  never 


STRABISMUS  403 

find  anything  of  the  kind.  If  the  limit  is  sometimes  displaced 
a  little  inwards,  this  is  due  to  a  lack  of  habit,  since  we  never 
have  occasion  to  make  so  great  a  motion  with  the  strabismic  eye. 
Hansen-Grut  distinguishes  between  the  position  of  anatomic 
equilibrium  and  the  position  of  functional  equilibrium  of  the 
eyes.  The  former  is  the  position  which  the  eyes  assume  apart 
from  all  nervous  influence.  When  the  eyes  are  in  this  position 
(during  sleep,  after  death,  etc.),  the  visual  lines  diverge  in  nearly 
all  patients.  The  position  of  functional  equilibrium  is  the  posi- 
tion which  the  eyes  assume  when  we  look  at  a  distant  object 
with  one  eye  covered.  In  this  position  the  visual  lines  are 
parallel  in  normal  persons.  The  convergent  strabismus  is  due 
to  the  fact  that  there  is  developed  an  unusual  position  of  func- 
tional equilibrium;  the  divergent  strabismus,  on  the  contrary, 
is  due  to  the  fact  that  such  a  position  is  not  developed  at  all,  so 
that  the  eyes  are  placed  in  the  position  of  anatomic  equilibrium. 

137.  Vision  of  Strabismic  Patients. —  Except  in  cases  of  con- 
vergent strabismus  of  myopes,  strabismic  patients  do  not  gen- 
erally complain  of  diplopia;  they  suppress  the  image  of  the 
deviated  eye,  so  that  the  strabismic  eye  serves  only  to  slightly 
increase  the  visual  field.  We  may,  however,  always  cause  diplo- 
pia by  holding  a  red  glass  in  front  of  the  good  eye,  by  keeping 
this  eye  closed  for  some  days,  etc. ;  but  then  we  often  meet  with 
the  singular  phenomenon  termed  paradoxical  diplopia.  This 
diplopia  was  discovered  by  v.  Graefe.  Examining  persons  af- 
fected with  convergent  strabismus,  in  whom  he  had  performed 
a  tenotomy  which  partly  corrected  the  defect,  he  found  crossed 
diplopia,  although  the  visual  lines  were  still  convergent,  and  the 
patients,  according  to  the  ordinary  rule,  should  have  indicated 
homonymous  diplopia.  Javal  was  the  first  to  study  this  phe- 
nomenon on  patients  not  operated  on.  The  explanation  of  this 
fact  is  that  there  is  developed  what  has  been  very  improperly 
named  a  vicarious  fovea.  The  patient  has  first  cultivated  the 
habit  of  suppressing  the  image  of  the  strabismic  eye ;  then  there 
is  gradually  formed  an  idea  of  the  false  position  of  the  strabismic 
eye;  he  has  learned  that  an  object  which  forms  its  image  on  the 


404  PHYSIOLOGIC  OPTICS 

fovea  of  the  good  eye,  forms  its  image  at  a  point  (b)  inwards 
from  the  fovea  of  the  strabismic  eye,  and  he  has  learned  to 
localize  this  image  at  the  place  where  the  object  to  which  it 
belongs  is  situated.  If  we  place  a  prism,  apex  down,  in  front 
of  the  good  eye,  the  patient  sometimes  says  that  he  sees  only 
the  image  of  the  strabismic  eye;  the  patients  localize  it  almost 
on  the  same  vertical  line  as  the  image  of  the  good  eye,  instead 
of  indicating  widely  separate  homonymous  images.  It  is,  there- 
fore, as  if  there  was  developed  a  correspondence  between  the 
point  b  and  the  fovea  of  the  good  eye.  But  the  localization  of 
the  image  is  always  very  uncertain;  the  patient  sometimes  says 
that  he  sees  both  images  well,  but  that  it  is  impossible  to  tell 
which  is  the  image  of  the  strabismic  eye. 

If  we  perform  a  tenotomy  which  does  not  completely  correct 
the  deviation,  the  image  of  the  point  fixed  is  no  longer  formed 
either  on  the  true  fovea  or  the  vicarious  fovea,  but  between  the 
two.  Patients  first  project  the  image  according  to  the  vicarious 
fovea:  as  it  is  formed  on  a  part  of  the  retina  situated  outside  of 
the  latter,  the  patient  sees  the  object  in  crossed  images.  Later, 
especially  if  we  make  systematic  exercises  in  order  to  reach  it, 
the  true  fovea  comes  to  exert  its  preponderating  influence:  the 
patient  sees  the  object  in  homonymous  images.  Following  the 
development  of  the  change  of  vision  of  the  patient,  we  some- 
times succeed  in  finding  a  time  when  the  patient  projects  the 
image  of  the  strabismic  eye  according  to  both  foveas  at  once: 
he  sees  with  the  strabismic  eye,  at  the  same  time,  one  image 
to  the  right  and  another  to  the  left  of  the  object.  This  singular 
form  of  vision  has  been  described  by  Javzl  under  the  name 
binocular  triplopia.  I  have  had  occasion  to  study  a  case  of  this 
character. 

138.  Treatment  of  Strabismus. — If  we  confine  ourselves  to  the 
treatment  by  operation,  it  is  prudent  not  to  completely  correct 
convergent  strabismus,  for  the  strabismic  eye  has  a  tendency 
to  put  itself  in  divergence,  a  tendency  which  sometimes  suffices 
by  itself  to  finally  cause  the  convergent  strabismus  to  disappear. 
On  the  contrary,  when  it  is  our  intention  to  reestablish  binocular 


STRABISMUS  405 

vision,  we  must  try  to  make  the  position  of  the  eyes  as  correct 
as  possible.  This  reestablishment  is  often  a  very  long  and  diffi- 
cult matter;  the  task  is  less  arduous  in  cases  in  which  there 
still  exists  binocular  vision  in  a  part  of  the  field.  In  certain  cases, 
such  as  the  periodical  divergent  strabismus  and  the  convergent 
strabismus  of  myopes,  we  succeed  by  means  of  some  exercises, 
or  even  by  the  simple  operative  treatment.  According  to  Javal, 
who  especially  devoted  his  attention  to  this  question,  the  course 
of  the  treatment  is  as  follows: 

a.  Reestablishment  of  diplopia  and,  if  possible,  of  the  vision 
of  the  strabismic  eye.    We  keep  the  good  eye  covered  by  means 
of  a  blind  patch;  if  the  vision  of  the  other  eye  is  very  bad,  in 
order  to  less  annoy  the  patient,  we  allow  him  to  wear  the  patch 
on  the  bad  eye  during  several  hours  of  the  day,  but  it  is  neces- 
sary, during  this  period  of  treatment,  never  to  allow  the  two 
eyes  to  be  uncovered  at  the  same  time,  under  penalty  of  never 
seeing  the  neutralization  disappear  or  of  seeing  the  strabismus 
increase ;  for,  as  the  diplopia  annoys  so  much  less  as  the  images 
are  more  distant  from  each  other,  the  patient  tries  to  squint 
more  strongly  in  order  to  separate  the  images. 

b.  Reestablishment  of  the  approximately  correct  position  of 
the  eyes  by  way  of  operation. 

c.  Stereoscopic  exercises. — We  begin  by  placing  in  each  field, 
on  each  visual  line,  a  round  spot.    If  the  patient  fuses  them,  we 
move  them  farther  or  nearer,  in  order  to  develop  in  him  the 
necessity  of  seeing  single.     The  stereoscope  of  Javal,  an  imita- 
tion of  that  of  Wheatstone  (fig.  189),  but  with  a  variable  angle 
between  the  mirrors,  lends  itself  very  well  to  this  exercise.    As 
soon  as  the  patient  sees  double,  we  begin.     When  the  patient 
has  succeeded,  we  make  him  fuse  letters  by  giving  him  smaller 
and  smaller  characters.     For  all  these  tests  it  is  necessary  to 
add  to  each  figure  numerous  small  marks,  different  ones   for 
each  eye,  in  order  to  make  certain  that  the  patient  really  fuses. 
He  ought  to  see  the  figure  with  both  series  of  marks ;  otherwise, 
he  neutralizes  one  of  the  figures,  instead  of  fusing  both.    When 
beginning  these  exercises,  we  often  encounter  the  phenomenon 
which  v.  Graefc  designated  under  the  name  of  antipathy  to  single 


406  PHYSIOLOGIC  OPTICS 

vision.  When  we  place  the  round  spots  in  positions  correspond- 
ing to  the  visual  lines,  the  patient  converges  or  diverges  in  order 
not  to  fuse  them;  if  we  try,  in  this  new  position  of  the  eyes, 
he  makes  his  convergence  change  again,  and  so  forth.  Javal 
invented  a  very  ingenious  card  to  surmount  this  difficulty,  which 
is  often  very  great. 

d.  Exercises  without  the  stereoscope. — There  often  exists  a 
part  of  the  field  in  which  the  patient  sees  single;  then  we  make 
him  exercise  in  order  to  increase  this  part,   for  example,  by 
placing  a  candle  in  the  part  of  the  field  in  which  the  patient  fuses 
and  bringing  it  towards  the  other  part;  when  the  patient  sees 
double,  we  begin  again. 

e.  If  the  patient  stands  these  different  tests,  we  begin  to  make 
him  do  controlled  reading.     We  interpose  a  pencil  between  the 
eyes  and  the  book;  reading  can  then  take  place  without  inter- 
ruptions only  by  using  both  eyes.     This  exercise  must  be  con- 
tinued for  months.    It  is  only  a  long  while  after  the  reestablish- 
ment  of  binocular  vision  that  the  patient  can  see  relief. 

Bibliography. —  Bohm.  Das  Schielen.  Berlin,  1845. — v.  Grafe  (A.). 
Weber  Doppeltschen  nach  Schieloperationen  und  Incongruenz  der  Netzhaiite. 
Arch.  f.  Ophth.,  I,  1,  p.  82. — v.  Grafe  (A.).  Ueber  eigenthiimliche  zur  Zeit 
noch  unerklarliche  Anomalien  in  der  Projection  der  Netzhautbilder.  Arch, 
f.  Ophth.,  II,  1,  p.  284. — v.  Grafe  (A.).  Symptomenlehre  der  Augen- 
muskelldhmungen.  Berlin,  1867. — Donders  (F.  C.).  Anomalies  of  the  Ee- 
fraction  and  Accommodation  of  the  Eye.  London,  1864.  Hansen-Grut  (E.). 
Pathogeny  of  concomitant  squinting  (Bowman  lecture).  Transactions  of 
the  Ophthalmological  Society  of  the  United  Kingdom,  Vol.  X,  1890. — Javal 
(E.).  Manuel  du  strabisme.  Paris,  Masson,  1896. 


CHAPTER   XXV 

OPTIC  ILLUSIONS 

139. — We  designate  by  the  above  name  cases  in  which  the 
visual  impressions  give  rise  to  a  false  judgment  on  the  nature 
of  the  object.  Illustrations,  paintings  and,  generally,  all  repre- 
sentations of  an  object  have  the  effect  of  producing  these  illu- 
sions; and  all  optic  instruments  act  in  a  like  manner.  In  the 
former  part  of  the  book  I  have  mentioned  several  times  illusions 
of  a  more  special  character;  I  shall  here  describe  briefly  some 
others,  the  explanation  of  which,  in  most  cases,  is  quite  obscure. 

a.  A  first  series  of  illusions  is  based  on  the  fact  that  a  line 
or  space  seems  larger  when  it  is  divided  than  when  it  is  not. 
This  is  the  reason  why  the  two  parts  ab  and  be  of  the  line  (fig. 


Fig.  195. 

195)   have  the  same  length,  but  that  still  the  part  be  appears 
longer,  because  it  has  divisions.    The  two  illustrations  of  figure 


Fig.  196. 

196  are  square,  but  the  illustration  a  seems  wider  and  the  illu- 
stration b  higher,  on  account  of  the  divisions.  For  the  same 
reason,  a  space  filled  with  furniture  appears  larger  than  when 

it  is  empty. 

407 


408 


PHYSIOLOGIC  OPTICS 


b.  Very  small  angles  are  estimated  to  be  larger  than  they  are 
in  reality.    The  following  illusions  may  be  considred  as  examples 
of  this  rule.    The  lines  ab  and  cd  of  fig- 
ure 197  are  situated  in  the  prolongation 
of  each  other,  but  cd  seems  displaced  up- 
wards.     The    illusion   increases    if    we 
move  the  figure  farther  away.    We  may 
conceive  that  if  we  judge  the  acute  angle 
to  be  too  large,  the  line  cd  ought  to  seem 
to  have  undergone  a  rotation  around  the 
point  c,  the  line  ab  around  the  point  b, 
which    would    produce   the    illusion 
question. 

The  same  error  of  judgment  seems  to 

''take  place  in  the  illusion  produced  by  the  designs  of  figure  198 
(Bering)  and  figure  199  (Zollner). 

In  figure  198  the  long  lines  are  straight  and  parallel,  but  seem 
curved ;  in  the  upper  part  of  the  figure  they  appear  to  have  their 
concave  sides  turned  towards  each  other;  in  the  lower  part  the 


Fig.  197. 


Fig.  198. 

contrary  takes  place.  In  the  figure  of  Zollner,  the  long  straight 
lines,  which  are  parallel,  seem  to  converge  or  diverge  upwards, 
following  the  direction  of  the  small  oblique  lines.  We  can  con- 
ceive that  these  illusions  would  be  produced  if  the  judgment  at- 


OPTIC  ILLUSIONS  499 

tributes  a  too  large  size  to  the  acute  angles.    According  to  Helm- 


:** 

5 


i 

5 
5 
! 
j» 

^\ 


W 

i'\ 

til 


M 

js 
o 

^  ^ 

o 

^  N 

5^ 


i 


5 
i 


II 


Fig.  199. 

holts,  the  movements  of  the  look  play  a  great  part  in  the  pro- 
duction of  these  illusions;  they  appear  much  more  pronounced 


\/ 


Pig.  200. 


if  we  keep  the  look  quiet.    If  we  bring  a  point  slowly  from  right 
to  left  in  front  of  the  figure  of  Zollner,  while  fixing  it  with  the 


410 


PHYSIOLOGIC  OPTICS 


look,  the  lines  seem  to  move ;  those  which  appear  to  incline  their 
upper  extremity  to  the  right  seem  to  ascend,  while  the  others 
seem  to  descend,  and  the  inclination  seems  at  the  same  time 
more  pronounced.  If  we  bring  the  point  from  left  to  right,  the 
lines  affect  reverse  movement.  The  experiment  is  not  very 
easy  to  perform,  but  we  can  obtain  the  same  effect  more  easily 
by  keeping  the  point  which  we  fix  motionless  and  moving  the 
drawing. 


Fig.  201. 

c.  The  two  long  straight  lines  of  figure  200  have  the  same 
length,  but  b  appears  smaller  than  a. 

d.  We  frequently  estimate  cylinders  too  large.     If  we  place 
a  large  bottle  on  a  sheet  of  paper,  and  trace  its  circumference, 
we  can  with   difficulty  conceive,   after  having  taken  away  the 
bottle,  that  we  are  not  deceived,  so  small  is  the  circle.    Another 
error  of  judgment  is  well  known:  we  present  a  tall  hat  to  some 
one,  asking  him  to  indicate  on  the  wall  its  height,  starting  from 


OPTIC  ILLUSIONS  411 

the  ground.    Generally  the  height  pointed  out  is  about  half  too 
large. 

e.  I  have  already  mentioned  the  reverse  of  relief  which  we 
observe  when  we  change  the  stereoscopic  images  sideways,  and 
which  is  known  under  the  name  of  pseudoscopia.  We  sometimes 
observe  the  same  phenomenon  under  other  circumstances.  If, 
for  example,  we  fix  with  one  eye  the  posterior  part  of  the  upper 
border  of  a  lamp  chimney,  we  obtain  quite  easily  the  illusion 
that  this  part  is  in  front,  and  the  glass  seems  at  the  same  time 
to  lean  towards  the  observer. — Observing  with  one  eye  the  cast 
of  a  medal,  it  may  be  difficult  to  tell  whether  the  figure  is  hollow 
or  in  relief. 

Analogous  phenomena  often  present  themselves  in  cases  in 
which  a  drawing  may  be  interpreted  in  two  different  ways.  Thus 
figure  20 1  seems  composed  of  cubes,  the  illuminated  side  of 
which  is  turned  sometimes  to  the  right,  sometimes  to  the  left. 
When  one  interpretation  has  predominated  for  a  certain  time, 
the  other  suddenly  presents  itself.  We  can  instigate  the  change 
by  quickly  imagining  the  contrary  relief. 

/.  We  mention,  finally,  the  illusions  of  movements  of  exterior 
objects,  which  often  present  themselves  in  consequence  of  the 
false  judgment  of  the  movements  which  we  ourselves  make.  One 
of  the  best-known  examples  is  that  of  the  apparent  movements 
of  objects  when  we  are  traveling  by  rail;  the  traveler  does  not 
take  into  account  his  own  change  of  position  and  attributes  the 
movement  to  the  exterior  objects.  The  reverse  illusion  often 
presents  itself  when  one  train  stops  alongside  of  another;  if 
the  latter  is  put  in  motion,  we  often  attribute  the  movement  to 
our  own  train.  Waltzers  see  exterior  objects  rotate  around  them 
in  a  direction  contrary  to  their  own  rotation.  The  movement 
seems  to  continue  for  some  time  after  stopping,  on  account  of 
the  persistence  of  the  jerking  movements  of  the  eyes  (page  360). 

Generally,  exterior  objects  do  not  appear  to  be  displaced  during 
the  movements  of  the  look,  but  if  we  bring  the  look  quickly 
from  one  of  the  limits  of  the  field  to  the  other,  exterior  objects 
seem  to  move  in  the  contrary  direction. 


412  PHYSIOLOGIC  OPTICS 

Aubert  has  described  the  following  illusion,  which  is  due  to 
a  like  reason.  In  the  shutter  of  a  completely  dark  room  we 
make  a  vertical  slit,  which  is  then  the  only  object  visible.  Lean- 
ing the  head  towards  one  of  the  shoulders,  the  slit  seems  to 
undergo  a  rotation  in  the  reverse  direction;  it  no  longer  appears 
vertical.  We  judge  the  inclination  of  the  head  to  be  less  than 
what  it  is,  almost  in  the  same  manner  as  the  movements  which 
we  cause  the  eyes  to  make  while  keeping  the  lids  closed,  always 
seem  less  than  they  really  are.  The  experiment  also  succeeds 
outside  of  the  dark  room,  especially  if  we  place  ourselves  in 
such  a  way  as  not  to  see  any  other  lines,  the  direction  of  which 
we  know  to  be  vertical. 


Bibliography. —  Zollner.  Ueber  eine  neue  Art  von  Pseudoscopie.  Pogg. 
Ann.,  CX,  p.  500. — Hering  (E.).  Beitrage  zur  Physiologic.  Leipzig,  1861, 
I,  p.  65. — Aubert  (H.).  Physiologic  der  Netzhaut.  Breslau,  1865. 


TREATISES  TO  CONSULT 


(Euvres  ophtalmologiques  of  THOMAS  YOUNG,  translated  and  annotated 
by  M.  TSCHEENING.  Copenhagen,  Hoest,  1894.  The  memoires  of  Young 
were  published  at  the  beginning  of  the  century  in  the  Transactions  of  the 
Eoyal  Society  of  London  and  reprinted  in  his  Lectures  (London,  1807). 
A  later  reprint  in  Peacock  Works  of  Thomas  Young,  London,  1855,  is  not 
to  be  recommended,  the  reproduction  therein  of  the  pretty  illustrations 
of  Young  being  quite  defective.  The  works  of  Young  are  often  of  a  very 
difficult  reading,  but  many  of  the  modern  ideas  on  ocular  dioptrics  and 
on  the  vision  of  colors  dated  from  him.  On  account  of  the  great  importance 
of  the  works  of  Young,  I  have  published  a  French  edition  of  them  which 
I  have  tried  to  make  of  an  easier  reading  by  explanatory  notes. 

v.  HELMHOLTZ  (H.).  Handbuch  der  physiologischen  Optik.  Leipzig, 
1867.  This  monumental  work  is  indispensable  to  all  those  who  desire  to 
make  a  profound  study  of  physiologic  optics,  but  it  is  not  a  very  easy 
study.  The  book  contains  nearly  all  that  was  known  on  the  subject  of 
physiologic  optics  at  the  time  of  its  appearance  and  a  complete  bibliogra- 
phy. In  1885,  the  author  began  a  new  edition  of  it  (Leop.  Voss,  Ham- 
burg), which  was  continued  after  his  death  by  A.  KCENIG.  The  only 
difference  between  it  and  the  former  consists  of  a  number  of  intercalations, 
which,  however,  are  not  of  very  great  importance,  if  we  except  those  of 
the  second  part  which  contain  the  results  of  the  researches  on  the  vision 
of  colors  of  Kcenig,  Dieterici,  Brodhun,  Uhthoff,  etc.  The  latter  portion 
of  the  work  contains,  from  the  hand  of  Koenig,  a  complete  bibliography, 
which  will  be  very  useful  to  the  investigators  of  the  future. — The  work 
of  HELMHOLTZ  was  translated  into  French  by  E.  JAVAL  and  N.  T.  KLEIN 
(Masson,  1867),  but  this  translated  edition  is  exhausted.— The  student  of 
physiologic  optics  must  not  dispense  with  reading  the  original  memoirs  of 
this  great  scholar. 

HERMANN  (L.).  Handbuch  der  Physiologic  der  Sinnesorgane.  2  vol. 
Leipzig,  1879.  The  part  which  has  to  do  with  vision  has  been  treated 
by  FICK  (A.)  (Dioptrics),  KUEHNE  (Chemistry  of  the  Retina)  and  HEKINO 
(E.)  (Movement  of  the  Eyes,  Binocular  Vision). 

Less  important  works  and  of  an  easier  reading: 

FICK  (A.).  Lehrbuch  der  Anatomie  und  Physiologic  der  Sinnesorgane. 
Lahr,  1864. 

KAISER  (H.).  Compendium  der  physiologischen  Optik.  Wiesbaden 
1872.  Apart  frtom  some  parts  which  the  author  has  treated  in  an  original 
manner,  this  work  is  an  extract  from  v.  HELMHOLTZ. 

413 


414  PHYSIOLOGIC  OPTICS 

AUBERT  (H.).  Physiologische  Optik,  in  Handbuch  der  gesammten 
Augenheilkunde  von  A.  GRAEFE  und  TH.  SAEMISCH.  Leipzig,  1876.  The 
most  original  part  is  an  extract  from: 

AUBERT  (H.).  Physiologic  der  Netzhaut.  Breslau,  1865,  a  book  which 
contains  a  great  number  of  very  elaborate  researches  on  the  retinal 
functions. 

LE  CONTE  (JOSEPH).  Sight.  London,  1881.  In  spite  of  some  errors 
this  work  is  very  instructive  on  account  of  its  originality. 

From  the  time  prior  to  v.  HELMHOLTZ  dates  MACKENZIE  (W.).  The 
Physiology  of  Vision.  London,  1841,  being  based  especially  on  the  works 
of  YOUNG  and  WHEATSTONE. 

What  was  known  on  the  subject  of  physiologic  optics  in  the  last 
century  is  found  in: 

PORTERFIELD  (WILLIAM).  A  Treatise  on  the  Eye.  2  vol.  Edinburgh, 
1759,  and  in: 

JURIN  (JACQUES).  Essai  sur  la  vision  distincte  et  indisti/ncte  in  the 
great  treatise  on  optics  of  EGBERT  SMITH  (A  Complet  System  of  Opticks}. 
London,  1738.  In  French  Cours  complet  d'optique  of  EGBERT  SMITH,  trans- 
lated by  PEZENAS.  Paris,  1767. 

The  work  of  JURIN  on  indistinct  vision  is  still  the  best  on  this  some- 
what neglected  question. 

Of  the  works  on  more  or  less  important  branches  of  physiologic  optics 
we  may  cite : 

BONDERS  (F.  C.).  On  the  Anomalies  of  Accommodation  and  Refraction 
of  the  Eye.  London,  1864.  In  German  by  O.  BECKER.  Wien,  1866.  In 
French  by  E.  JAVAL,  in  DE  WECKER.  Traite  des  maladies  des  yeux.  Paris, 
1866.  On  account  of  its  remarkable  clearness  BONDERS  is  of  a  very  easy 
reading,  and  may  be  recommended  to  every  young  medical  student  who 
desires  to  begin  the  study  of  this  branch  of  opthalmology. 

The  same  subject  has  been  treated  in: 

NAGEL  (A.).  Die  Anomalien  der  Refraction  und  Accommodation  des 
Auges  in  Grdfe  und  Sdmisch.  Handbuch  der  Augenheilkunde.  Leipzig, 
1880. 

LANDOLT  (E.),  in  DE  WECKER  and  LANDOLT.  Traite  complet  d'ophtal- 
mologie,  1884. 

MAUTHNER  (L.).  Vorlesungen  ilber  die  optischen  Fehler  des  Auges. 
Wien,  1876. 

MAUTHNER  (L.).  Farbenlehre.  Second  edition.  Wiesbaden,  1894. 
The  books  of  Mauthner  are  written  in  a  very  clear  style  and  bear  the 
impress  of  great  learning. 

Memoires  d'ophtalmometrie,  annotated  and  preceded  by  an  introduc- 
tion by  E.  JAVAL.  Paris,  M&sson,  1890.  This  work  contains  a  great 
number  of  notes  on  ophthalmometry  by  different  authors. 

E.  JAVAL.  Manuel  de  Strabisme.  Paris,  Masson,  1896.  This  work 
is  important  for  the  study  of  binocular  vision. 


INDEX 


Abduction,  363 

Aberration,     chromatic,     96,     120, 
131,   133,   137 

produced    by    accommodation, 
211 

spherical,  96,  114,  125 
Aberroscope,  the,  123 
Aberroscopic  phenomena,  172,  173, 

206 

Absorption  of  light,  2 
Accommodation,  46 

amplitude  of,  97,  192 

astigmatic,    155 

author's  theory  of,  200 

central  and  peripheral,  208 

Cramer's  theory  of,  197 

Helmholtz  theory  of,  198 

H.  Muller  's  theory  of,  199 

influence  of,  377 

mechanism  of,   195,   196,  198, 
201 

paralysis  of,  194 

relative  amplitude  of,  365 

skiascopic  examination  of,  209 

spasm  of,  194 

Young's  theory  of,  201 
Accommodation    and    convergence, 

relation  between,  365 
Achloropsia,  322 
Acuity,  visual,  335 

peripheral,  341 
Adduction,    363 
Aerial  images,  42 

perspective,  378 
After-images,  291 

positive,   291 

negative,  291 
Akyanopsia,  323 
Amblyopia  exanopsia,  401 
Ametropia,  9 
Anaglyphs,  338 
Anerythropsia,  322 
Angle  alpha,  45,  77 

critical,  11 

meter,  364 

of  convergence,  12 

of  deviation,  12 

of  incidence,  2 


Angle  of  refraction,  2 

of  visibility,  336 
Aniridia,  198 
Antagonism   of    the    visual    fields, 

389 

Aperture  of  an  optic  system,  41 
Aphakia,  96,  111 

Asthenopia,    accommodative,    109, 
193 

of  astigmatic  patients,  158 

tarsal,  177 

Astigmatic     persons,    examination 
of,  159 

surfaces,  75 
Astigmatism,  138,  166 

against  the  rule,  150 

by  incidence,  115,  143 

crystalline,  150 

corneal,  147,  149,  151 

irregular,  96,  164,  166 

latent,  155 

oblique,   147 

of  the  human  eye,  145 

physiologic,  146 

post-operative,  156 

produced  by  the  form  of  the 
surfaces,  138 

regular,  96,  138,  141 

ophthalmometric    and    subjec- 
tive, 150 

supplementary,  151 

symptoms  of,  158 

with  spherical  aberration,  169 

with  the  rule,  150,  158 
Arteries,  pulsation  of,  240 
Atropine,  255 
Auto-ophthalmoscope,  241 


Base  line,  364 

Binocular  ophthalmoscope,  387 

Binocular   vision,   346 

projection  in,  369 

theories  of,  391,  393,  395 
Black,  sensation  of,  287 

absolute,  287 
Brightness,  284 
Brushes  of  Haidinger,  187 


415 


Cardinal  points,  23 

methods  of  finding,  25,  26 

of  the  crystalline  lens,  29 

of  the  human  eye,  39 
Cataract,  203,  281 
Cat 's  eye,  amaurotic,  229,  230 
Centering,  defect  of,  80 
Characteristic  part  of  a  pencil  of 

light,  167 

Chess-board  of  Helmholtz,  260 
Chromatic  aberration,  96,  120,  131, 
133,  137 

correction  of,  137 
Chromatoptometer  of  Chibret,  325, 

326 

Ciliary  corona,  188 
Ciliary  muscle,  discovery  of,  203 

structure  of,  205,  224,  225 
Cocaine,  255 
Color-blindness,   317 
Color-box  of  Maxwell,  299,  305 
Color  curves  of  Maxwell,  306 

of  a  dichromatic,  321 
Color  phenomena  of  contrast,  287, 

290 
Colors,  complementary,  287 

equation  of,  298 

methods  of  mixing,  298 

results  of  mixtures  of,  301 

sensations  of,  285 

spectral,  298 

the  principal,  328 

the  standard,  305 
Color  sense,  282 

clinical  examination  of,  324 
Color  table  of  Helmholtz,  313 

of  Maxwell,  304,  308,  319 

of  Newton,  285,  303 
Color  vision,  mechanism  of,  327 

Ebbinghaus's  theory,  331 

Helmholtz   theory,   329 

Bering's    theory,    330 

Koenig's  theory,  331 

Parinaud's  theory,  331 

Young's  theory,  327 
Concave  spherical  mirrors,  4 

aperture  of,  4 

apex  of,  4 

axis  of,  4 

principal  focus  of,  4 

principal  focal  distance  of,  4, 

reflection  on,  5 
Conjugate  points,  2,  6 
Conoid  of  Sturm,  138 
Contact  glasses,  174 
Contact  of  corneal  images,  59 
Controlled  reading,  405 


Convergence,  defect  of,  363 

measurement  of,  363 

negative,  362 
Convex  mirrors,  7 
Co-ordinates,  center  of,  369 

polar,  369 
Cornea,  basilar  part  of,  67 

conical,  66 

examination      of      peripheral 
parts  of,  67 

increase  in  curvature  of,  195 

in  keratonconus,  72,  73,  74 

optic  part  of,  67 

refracting  power  of,  38,  69 

results  of  measurements  of,  66 

utilized  part  of,  65 
Crystalline  lens,  34 

accommodative  layer  of,  222 

advance  of,  195 

astigmatic  accommodation  of, 

153 

Crystalline   lens,   catoptric  images 
of,   196,  197 

change  in  thickness  of,  219 

contents  of,  222 

cortical  portion  of,  36 

deformity    of,    during    accom- 
modation, 216 

increase  in  curvature  of,  195 

measuring  aberration  of,   128 

measuring  surfaces  of,  81,  82, 
83,  84 

luxation  of,  96 

nucleus  of,  36,  222 

obliquity  of,  153 

refracting  power  of,  38 

total  index  of,  37 
(Cylindrical  glasses,  145,  158 
Czermak,  experiment  of,  90 


Daltonism,  317 

bilateral,  318 

monolateral,  318 
Decentered  eyes,  158 
Deformity  of  internal  surfaces  in 

astigmatism,  151 
Descartes,  law  of,  9,  25 
Dichromasia,  377,  320 
Dichromatopsia,  377 
Diffraction  in  the  eye,  188 
Diffusion  circles,  88,  117,  207 

size  of,  88 

examination  of,  117 
Diplopia,     physiologic     binocular, 
370 

paradoxical,  390 
Disc  keratoscopic,  74 

of  Benham,  277 


416 


Disc  of  Helmholtz,  277 

of  Masson,  276 

of  Placido,  74 

of  Volkmann,  356 
(Dispersion,  131,  136 
Distance,    indirect    judgment    of, 
377 

sensation  of,  401 
Doubling,  methods  of  in  ophthal- 

mometry,  59 
Dove,  experiment  of,  289 


Empiric  theories,  261 
Entoptic  phenomena,  176 
analysis  of,  180 
manner  of  observing,  176 
parallax  of,   181 
Entoptic  object,  determination  of 

position  of,  182 
examination  of  refraction  of, 

182 
Entoptic  observation  of  vessels  of 

retina,  183 

Entoptoscope,  the,  180 
Eye,  an  artificial,  262 

aperture  of  the  optic  system 

of  the,  41 

color  of  fundus  of  the,  239 
center  and  axes  of  rotation  of, 

346 

directing,  371 
emmetropic,  97 

methods  of  illuminating   fun- 
dus of  the,  229 
muscles  of,  248 
Eye,  optic  axis  of  the,  45 

optic  constants  of  the,  33 
optic  system  of  the,  33,  38 
schematic,  of  Helmholtz,  34 
the  simplified,  32 
Eyes,  associated  movements  of  the, 

361 

jerking  movements  of  the,  360 
relative  movements  of  the  two, 

360 

rotary  movements  of,  358 
Erect  image,  examination  by,  233, 

237 

Eserine,  255 
Exophoria,  399 


F 

Far  point,  97 
Fixation,  point  of,  44 


Fechner,  law  of,  270 

explanation  of  the,  270 

verification   of   the,   270,   271. 

272,  273,  274 
Focal  distance,  anterior,  23 

of  a  convex  mirror,  7 

of  a  concave  mirror,  8 

posterior,    13,   23 

principal,  4 
Focal  interval  of  Sturm,  195 

lines,  138,  139,  171 
Focus,  anterior,  23 

posterior,  23 

principal,  4,  5 
Form  sense,  the,  273 

measure  of  the,  272,  336 
Foucault,  principle  of,  119 
Fovea,  44,  95,  238,  270,  279 
Fraunhofer,  experiments  of,  134 

lines  of,  132,  283,  295 


G 


Gauss,  theory  of,  23,  41 

Glabella,  373 

Globe,  elongation  of,  195,  202 


Hemeralopia,  280 

Hess  and  Heine,  observations  of, 

218,  226 

Homatropine,  255 
Hooke,   experiments  of,   234,  235, 

236 

Horopter,  374 
Hue,  of  color,  284 

changes  of,  284 
Hypermetropia,  96,  99,  109 

absolute,  109 

axial,  95 

correction  of,  99 

latent,  109,  233 
Hypoconchia,  104 


Iconoscope  of  Javal,  386 
Identical  points  of  the  retina,  391 
Identity,  theories  on  the  nature  of, 

391 
Image,  2 

defects  of  the,  141 

erect,  examination  by,  232,  2; 

inverted,  examination  by,  241 

of  mirrors,  3,  4,  5 

of  lenses,  18 


417 


Image  of  any  optic  system,  24 

produced  by  a  small  aperture, 
2 

real,  2 

useful,  46 

virtual,  2 

Images,    displacement    of    in    ac- 
commodation,  217,  218 

manner  of  observing  the,  50, 
54 

of    Purkinje,    34,   35,   48,    50, 
78,  79 

of  the  eye,  false,  47 

of  the  second  order,  false,  54 

suppression  of  double,  375 
Innervation,  judgment  of,  367 
Intensity,   284 

Inter-focal  distance,  138,  139 
Internal  surfaces,  position  of,   80 

centers  of,   83 

deformity  of,  151 
Interval  of  an  optic  system,  27,  30 
Inverted    image,    examination    by, 

241 
Iris,  197 

apparent,  41 
Iridodonesis,  257 
Isopters,  242 


Jaeger,  test-types  of,  338 
Javal,  test  chart  of,  338 
Judgment,  unconscious,  377 


Keratoconus,  96,  157,  213,  214 
Keratoscope    of    de    Wecker    and 

Massilon,  213 
Keratoscopic  disc,  74 

image,  73,  74,  75,  76 


Lens,  17 

achromatic,  133 
aplanatic,    114 
axis  of,  17 
concave,  19 
crossed,  115 
crown,  115 
flint,  115 

focal  distance  of  a,  17,  20 
infinitely  thin,  17,  28 
measuring    focal    distance    of, 
20 


(Lens,  optic  center  of,  17 

over-corrected,   114 

phenomena       dependent       on 
spherical  aberration  of,  115 

refracting  power  of,  22 
Lenticonus,  96 

false,  96 

Leucoma,  central,  281 
Leucoscope,  the,  325 
Light,  harmful,  47 

lost,   47 

monochromatic,  188,  282 

quantity  reflected,  10 

rectilinear  propagation  of,  1 

useful,  47 
Light  sense,  the,  270 

measurement  of,  274 
Lithium  flame,  282 
Listing,  axes  of,  353 

law  of,  261,  262,  348,  349,  352, 

354,  357,  358 

Luminous   point,    analysis   of   the, 
171 

figures  of,  171 
Luminous  rays,  1 

incident,  4 

reflected,  4 


M 


Macula,  238,  281,  315 

Maddox  test,  399 

Meissner,  experiments  of,  335 

Menisci,  20 

Meridian,  apparently  vertical,  335 

Meter  angle,  364 

Meyer,  H.,  experiment  of,  287 

Micrometer,  237 

Microphthalmia,  67 

Mile,  experiment  of,  90 

Mires,  57 

Mirrors,  concave  spherical,  4 

plane,  3 

portion  of  used,  8 
Monochromasia,  324 
Muscse  volitantes,  179,  186 
Mydriatics  and  Myotics,  255 
Myopia,  96,  101,  107,  196 

atropine  treatment  of,  107 

axial,  95 

correction  of,  98 

dangerous,  102 

treatment  of,  107 


418 


N 


Nativistic  theories,  263 
Near  point,  98 

determination  of,   192 
Neutral  point  in  the  spectrum  of 

color-blind,  317 
Nicol  prism,  188 
Nodal  points,  23,  39 
Normal,  of  a  surface,  18 
Nyctalopia,  281 


O 


Oblique  illumination,  256 
Ocular  movements,  346,  360 
muscles,  action  of,  248 
Opaque  bodies,  1 
Ophthalmometer,  58,  59,  60 
of  Brudzewski,  72 
of  Helmholtz,  59,  68 
of  Javal  and  Sehioetz,  61,  68 
Ophthalmometry,  57 
Ophthalmodynamometer     of     Lan- 

dolt,  363 
Ophthalmophakometer,  53,  77,  211, 

216 

Ophthalmoscope,  229 
binocular,   387 
of  Coccius,  8 
of  Cramer,  196,  227 
of  Helmholtz,  231 
principle  of,  231 
Ophthalmoscopic     examination     of 

refracting  media,  245 
field,  236,  243 
magnification,  by  erect  image, 

233 

magnification  by  inverted  im- 
age, 241 

Ophthalmoscopy,  229 
Optic  axis,  45 

constants  of  the  eye,  33 
illusions,  407 
properties  of  bodies,  1 
Optic  system  of  the  cornea,  38 
of  the  crystalline  lens,  38 
of  the  eye,  38 
aperture  of  the  eye,  41 
obliquity  of  the  eye,  171 
Optogram,  270 
Optometer,   100 
of  Badal,   192 
of  George  Bull,  192 
of  Mile,  90 
of  Scheiner,  90 
of  Weiland,  162 
of  Young,  91,  172,  208 


Papillary  excavations,   237,   239 
Papilla,  237,  238,  286 

scleral  border  of,  239 
Paracentesis,  227 
Paracentral  shadow,  252 
theory  of,  251 
explanation  of,   252 
Parallax,  influence  of  the  binocu- 
lar, 382 
Penumbra,  2 
Perception    of    depth,    monocular, 

377 

binocular,  382 

Periscopic  glasses,  115,  162 
Phosphene  of  Czermak,  186 
Phosphorescence,  229 
Photoptometer  of  Charpenteir,  275, 

297 

of  Foerster,  275 
Placido,  disc  of,  74 
Plates  of  Helmholtz,  246 
Point  of  fixation,  44 
Position  of  anatomic  equilibrium, 

403 

of  cardinal  points,  30 
of  the  centers,  81 
of  the  surfaces,  80 
of    functional   equilibrium    of 

eye,  403 
Presbyopia,  193 
Primary  direction  of  eye,  349 

position,  349 
Principal   focus,  4 
focal  distance,  4 
meridians,  138 
planes,  24 
points,  23 

Prism,  achromatic,   132,   133 
a  vision  directe,  132,  133 
Nicol,  187 
refraction  by  a,  11 
with  total  reflection,  10 
Wollaston,  61 

Projection  in  binocular  vision,  369 
Projections,  center  of,  370 
general  laws  of,  366 
theory  of,  392 
Pseudoscope,  the,  386 
Pseudoscopia,  411 
Punctum  proximum,  92,  93 

remotum,  92,  93 
Pupil,  254 

apparent,  42,  254 
contraction  and  dilatation  of, 

254 

in  accommodation,  256 
influence  of  light  on,  255 
movements  of,  255 


419 


Pupil,  nerve  control  of,  254 

of  albinos,  230 

of  entrance,  43 

of  exit,  43 

real,  42 

variations  of  refraction  in,  173 
Purity  of  color,  284 


E 


Eadii,  direct  determination  of,  84 
Eadius  vector,  368 
Eagona  Scina,  experiment  of,  288 
Eeflection,  2 

images  of  the  eye,  211,  212 

regular,  2 

total,  10 

on  a  concave  mirror,  4,  5 

on  a  plane  mirror,  3 
Eefracting  surface,  power  of,  16 

simple,  28 
Eefraction,  10 

anomalies  of,  95 

by  a  parabolic  surface,  214 

by  a  prism,  12 

by  a  spherical  surface,  13,  14 

by  plane  parallel  plates,  11 

by  a  surface  of  revolution  of 
the  second  degree,  17 

index  of,  10 

in  the  pupil,  173 

ophthalmoscopic    and    subjec- 
tive, 237 
Eelief,  idea  of,  393 

measurement  of,  393 

theory  of,  393 
Eetina,  264,  266 

changes  of,  266 

detachment  of,  280 

functions  of,  266 

pigment  of,  267 

Eetina  of  frog,  section  of,  268 
Eetina    seen    by    the    ophthalmom- 

eter,  240 

Eetina 's  own  light,  272 
Eetinal  horizon,  354 
Betinal  purple,  239,  266 

discovery  of,  267 
Eetinal  oscillations,  293 


S 


Saturation  of  color,  284 
£cheiner,  experiment  of,  91,  115, 

300 

Scopolamine,  255 
Secondary  direction,  349 
Shade  of  color,  284 


Shadows,  1 

colored,  288 

deformity  of  the,  118 

experiments  with,  290 
Sight,  lines  of,  89 
iSkiascopic  examination   for   astig- 
matism, 160,  248 

field,  24,  25 

examination    of    optic    anom- 
alies, 252 
Skiascopy,  246 

application  of,  246 

with  concave  mirror,  248 

with  plane  mirror,  246 
£nellen,  charts  of,  337 
Sodium  flame,  282 
Spectacles,  choice  of,  104,  193 
Spectroscope,  282 
Spectrum,  282 

colors  of,  284 

of  diffraction,  283 

of  refraction,  284 
Spot  of  Mariotte,  76,  286,  342 
Spherical  aberration,  96,  114,  125 
Spherometer,  21 
Staphyloma,  237 
'^tenopaic  opening,  92 
Stereoscope,  382 

effect  of,  388 

of  Helmholtz,  386 

of  Wheatstone,  386 
Stereoscopic  exercises,  405 

images,  methods  of  observing, 
384 

lustre,  388 

parallax,  383 

photographs,  388 

Strabismic  patients,  vision  of,  403 
Strabismus,  397 

cause  of,  402 

concomitant,  397,  398,  400 

convergent,  of  myopes,  403 

latent,   398 

measurement  of,  400 

nature  of,  402 

paralytic,  397 

relation     between     convergent 
and  hypermetropia,  400 

relation  between  divergent  and 
myopia,  402 

treatment  of,  404 
Strontium  flame,  285 
Synchisis  scintillans,  246 
Syringe  of  Pravaz,  228,  257 


Tapetum,   229 
Telescopic  system,  27 


420 


Telestereoscope  of  Helmholtz,  387 
Thallium  flame,  282 
Threshold,  the,  274 

determination  of,  279 
Tint,  284 
Tore,  142,  163 
Translucent  bodies,  1 
Transparent  bodies,  1 
Trichromasia,  abnormal,  315 
Triplopia,  binocular,  404 
Troxler,  phenomenon  of,  292,  343 


Veins,  pulsation  of,  239 
Vision,  "  recurrent, ' '  292 

single,  antipathy  to,  405 
Visual  acuity,  335 

central,  334 


Visual,  measurement  of,  335,  336 
peripheral,  341 

Visual  acuity  and  illumination,  re- 
lation between,  340 

Visual  field,  projection  of  the,  366 

Visual   fields,   antagonism   of   the, 
276,  389 

Visual  impressions,  projection   of, 
366 

Visual  line,  44 

Volkmann,  disc  of,  356 
experiments  of,  120 


W 

White,  normal,  of  Koenig,  287 
Wbllaston,  experiment  of,   134 
prism  of,  61 


421 


LIST  OF  AUTHORS 


Abbe,  32,  34,  43 

Agabobon,   293 

Airy,  145 

Almeida  (d'),  388 

Argyll  Bobertson,  256 

Arlt,  104,  113,  196,  206,  226,  257, 

265 
Aubert,  68,  87,  314,  412,  413 

Babbage,  232 

Badal,  100,  101,  192,  243 

Becker,  56,  414 

Beer,  229 

Bellarminoff,  231,  253 

Benham,  278 

v.  Bezold,  137 

Bidwell,  292 

Bitzos,  252 

Bjerrum,  243,  253,  278,  281,  342, 

245 

Blix,  56 

Boehm,  110,  113,  400,  406 
Boll,  267,  269 
Bouguer,  271,  274,  281 
Bourgeois,  66 
Bouty,  32 
Bowman,  203,  228 
Brewster,  181,  182,  191,  384,  385, 

395 

Brodhun,  294,  333 
Brown-Sequard,  254 
Brudzewski,  72,  87,  126,  128,  130 
Bruecke,   132,  203,  228,  229,  232, 

253,  393,  396 
Bull  (George),  155,  159,  163,  177, 

178,  192,  193,  265 
Burkhardt,  338 
Burow,  184 

Charpentier,  275,  281,  293,  297 

Chibret,  326,  333 

Coccius,  56,  60,  100,  200,  226,  189, 

253 

Cohn,  102,  256,  325 
Coronat,  197 
Cramer,   196,   197,   198,  216,   218, 

219,  224,  227 
Cretes,  363,  400 
Crzellitzer,  190,  224,  228 
Cuignet,  246,  253 
Cumming,  229,  232,  253 
Czermak,  90,  187,  200 


Daae,   325 

Dalton,  317,  323,  332 

Darier,  178,  191 

Darwin,  264 

Davis,  292 

Demicheri,  35,  52,  96,  113,  173, 
209,  214,  222,  245,  253 

Descartes,  9,  26,  195 

Dieterici,  285,  312,  316,  321,  333 

Dimmer,  112,  113 

Dobrowolsky,  155 

Dojer,  346 

Dollond,  133 

Doncan,  181,  182,  191 

Donders,  61,  66,  100,  103,  106,  108, 
109,  110,  113,  146,  150,  163, 
181,  182,  189,  193,  203,  237, 
264,  316,  318,  346,  349,  352, 
358,  359,  365,  400,  406,  414 

Dove,  289,  388,  389 

Druault,  188,  189,  191 

Dubois   (Raphael),  59 

Dubois-Reymond,  256,  265,  269 


Ebbinghaus,  331,  333 
Eissen,  150 

Eriksen,  68,  70,  72,  87,  155 
Euler,  133 


Fechner,  270,  271,  272,  273,  274, 
275,  277,  279,  280,  293,  294 
Fick,  354,  359,  413 
Foerster,  205,  228,  275,  280 
Fontana,  205 

Fraunhofer,  132,  135,  137,  284,  297 
Fukala,  108 


Galien,  392 

Gariel,  32 

Gauss,  23,  32,  33,  41 

v.  Genderen  Stort,  268,  269 

Giraud-Teulon,  387,  388,  392 

Goulier,  146,  163 

v.  Graefe,  100,  129,  228,  241,  397, 

402,  403,  405,  406 
Graefe  (Alfred),  198,  228,  402,  406 
Green,  338 
Groenouw,  342,  345 
Guillery,  338,  342,  345 


423 


Haidinger,  187,  191 

Hamer,  66 

Hansen  Grut,  280,  397,  399,  401, 
402,  403,  406 

Hay,  352 

Heath,  32 

Heine,  218,  226,  228 

v.  Helmholtz,  6,  32,  34,  37,  57,  59, 
61,  66,  68,  95,  131,  135,  137, 
146,  178,  198,  199,  200,  203, 
205,  206,  219,  220,  222,  226, 
228,  229,  231,  232,  233,  246, 
253,  257,  260,  261,  262,  263, 
264,  277,  298,  301,  302,  313, 
322,  329,  330,  331,  332,  334, 
335,  337,  346,  349,  354,  359, 
378,  386,  387,  390,  395,  409, 
413,  414 

Hencke,  199 

Henle,  44 

Hensen,  199,  225 

Bering,  264,  324,  330,  331,  332, 
350,  358,  361,  372,  376,  408, 
412,  413 

Hermann,  153,  352,  413 

Herschel,  32 

Hess,  218,  226,  228 

Heuse,  56 

v.  Hippel,  318,  319,  329 

Hirschberg,  100,  400 

Hocquard,  222 

Holmgren,  322,  324 

Holth,  72,  74,  222,  343,  344,  345 

Home,  195 

Hooke,  334,  335,  336,  345 

Hueck,  198,  219,  228,  256,  358,  359 

Huyghens,  332 

Iwanoff,  226 

Jackson,  125,  130,  210,  253 

Jaeger,  241,  338 

Jamin,  32 

Javal,  44,  48,  60,  61,  62,  63,  66, 
68,  73,  75,  87,  100,  107,  137, 
146,  147,  150,  151,  153,  158, 
162,  165,  224,  278,  289,  338, 
339,  349,  356,  357,  359,  364, 
365,  371,  375,  376,.  386,  389, 
393,  395,  400,  401,  403,  404, 
405,  406,  413,  414 

Johnsson,  91 

Jurin,  94,  414 

Kagenaar,  60 

Kaiser,  371,  376,  413 

Kepler,  46,  195,  392 

Klein,  281,  413 

Knapp  (H),  146,  150,  163 


Knapp,  Jr.,  372  * 

Koanig,    285,    287,    294,    299,    312, 

316,  317,  321,  322,  326,  331, 

333 

Koster,  207,  209,  212,  220,  332,  333 
Krause,  221,  228 
Krenchel,  280,  281,  325,  333 
v.  Kries,  331,  333 
Kuehne,  267,  269,  413 


Laiblin,   187 

Lambert,  271,  281,  287,  301,  332 

Lamare,  360,  365 

Landolt,  113,  358,  363,  400,  414 

Langenbeck,  196,  228 

Leber,  322 

LeConte,  414 

(Leonardo  da  Vinci,  46 

Leroy,  237,  250,  251,  253 

Listing,  37,  46,  180,  191,  262,  348, 

349,  351,  352,  353,  354,  355, 

357,  358,  359,  374 
Lorenz,  32 


Mace  de  Lepinay,  294,  332 

Mackenzie,  414 

Maddox,  399 

Mannhardt,  204,  227 

Mariotte,  286,  342,  343,  344,  354 

Martin,  150,  155 

Msteeart,  95,  132 

Masselon,   147,  213 

Masson,   276,   277,   278,   280,   290, 

300,  313 

Matthiessen,  34,  37,  46,  68 
Mauthner,  61,  113,  200,  323,  414 
Maxwell,  298,  300,  302,  304,  305, 

306,  308,  309,  310,  312,  313, 

315,  316,  319,  320,  321,  328, 

329,  332 

Meissner,  355,  356,  359 
Meyer  (H.),  130,  287 
Mile,  90,  94 
Mjiller    (H.),   184,   185,  191,   199, 

203,  204,  205,  228,  266,  332 
Muller    (Joannes),   374,   375,   391, 

396 


Nagel,  364,  365,  396,  414 
Newton,  6,  98,  285,  287,  301,  302, 
303,  307,  312,  332,  392,  396 
Nicati,  294,  332 
Nordenson,  150,  163 


Ostwalt,  112,  113,  154 


424 


Panum,  392,  396 

Parent,  246,  250,  253 

Parinaud,  279,  296,  297,  331,  333, 

402 

Petit  (Jean  Louis),  221,  228 
Pfalz,  150 

Pfluger,  112,  287,  325 
Plaeido,  74,  147 
Porta,  46 

Porterfield,  392,  414 
Pouillet-Miiller,   32 
Pravaz,  228,  257 
Preyer,  323 
Prentice,  365,  400 
Purkinje,  48,  49,  50,  54,  56,  78,  97, 

183,     186,     190,     196,     200, 

227,  240,  257,  292,  293,  313, 

332 


Kaehlmann,  402 

Bagona  Scina,  288 

Eamsden,  195 

Eayleigh,  310,  316,  332,  379 

Bee,  166,  167,  168,  169,  170,  171, 

175 

Bisley,  105 

Bochon  Duvignaud,  228 
Bose,  326 
Buete,  241,  253,  358,  359 


Salomansohn,  188,  191 

Scheiner,  46,  91,  92,  94,  115,  120, 

195,  300 
Schioetz,    48,   60,    61,   62,    63,    68, 

147,  150,  163,  165,  188,  189, 

191,  224,  349,  400 
Schlemm,  204 
Schmidt-Bimpler,  245 
Schweigger,  163,  402 
(Seebeck,  322,  325,  332 
Smith  (Bobert),  345,  414 
Snellen,  101,  337,  338,  339 
Snellius,  9 
Sous,  100 
etadfeldt,   41,  46,   112,   128,   129, 

130,  224,  228,  257 
Steiger,  66 
Stellwag,  110,  113,  338,  345,  402 


Stilling,  104,  325 

Stokes,  162 

Sturm,  138,  158,  163,  195 

Sulzer,  67,  68,  70,  72,  87,  154,  155, 


Troxler,  292,  343,  344,  360 
Tscherning,  46,  56,  61,  87,  94,  113, 
130,  137,  163,  175,  191,  209, 
228,  265,  332,  345,  359 
Turk,  240 


Uhthoff,  332 


Vaeher,  155 
Verdet,  32 
Vierordt,   187 
Voelkers,  199,  225 
Volkmann,  120,  121,  130,  348,  356, 
357,  358,  359,  391,  392,  396 


Wecker   (de),  106,  147,  213,  246, 

400,  402 
Werlein,  91 
Weyde   (v.d),  321 
Wheatstone,    382,    385,    386,    392, 

395,  405,  414 
Wollaston,  60,  61,  134,  137,  162, 

392 
Wiillner,  32 


Young,  37,  46,  56,  91,  92,  121,  122, 
123,  124,  134,  135,  136,  145, 
165,  172,  173,  187,  188,  192, 
193,  201,  202,  203,  208,  209, 
237,  265,  289,  308,  327,  328, 
329,  331,  359,  377,  379,  381, 
413,  414 


Zeiss,  133 

Zinn,  223 

Zoellner,  408,  409,  412 

Zumft,  332,  333 


425 


540192 


physioloiic  optics 


.j; 

u3*HY 


540192 


QP 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


